# Preprocessing time : 0.012 s # Problem is unsatisfiable (or provable), constructing proof object # SZS status Theorem # SZS output start CNFRefutation. fof(8, axiom,![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', d3_tarski)). fof(27, axiom,![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', symmetry_r1_xboole_0)). fof(43, axiom,![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', t3_xboole_0)). fof(51, conjecture,![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', t63_xboole_1)). fof(57, negated_conjecture,~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))),inference(assume_negation,[status(cth)],[51])). fof(66, plain,![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))),inference(fof_simplification,[status(thm)],[43,theory(equality)])). fof(101, plain,![X1]:![X2]:((~(subset(X1,X2))|![X3]:(~(in(X3,X1))|in(X3,X2)))&(?[X3]:(in(X3,X1)&~(in(X3,X2)))|subset(X1,X2))),inference(fof_nnf,[status(thm)],[8])). fof(102, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&(?[X7]:(in(X7,X4)&~(in(X7,X5)))|subset(X4,X5))),inference(variable_rename,[status(thm)],[101])). fof(103, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)&~(in(esk3_2(X4,X5),X5)))|subset(X4,X5))),inference(skolemize,[status(esa)],[102])). fof(104, plain,![X4]:![X5]:![X6]:((~(subset(X4,X5))|(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)&~(in(esk3_2(X4,X5),X5)))|subset(X4,X5))),inference(shift_quantors,[status(thm)],[103])). fof(105, plain,![X4]:![X5]:![X6]:((~(subset(X4,X5))|(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)|subset(X4,X5))&(~(in(esk3_2(X4,X5),X5))|subset(X4,X5)))),inference(distribute,[status(thm)],[104])). cnf(108,plain,(in(X1,X2)|~in(X1,X3)|~subset(X3,X2)),inference(split_conjunct,[status(thm)],[105])). fof(170, plain,![X1]:![X2]:(~(disjoint(X1,X2))|disjoint(X2,X1)),inference(fof_nnf,[status(thm)],[27])). fof(171, plain,![X3]:![X4]:(~(disjoint(X3,X4))|disjoint(X4,X3)),inference(variable_rename,[status(thm)],[170])). cnf(172,plain,(disjoint(X1,X2)|~disjoint(X2,X1)),inference(split_conjunct,[status(thm)],[171])). fof(215, plain,![X1]:![X2]:((disjoint(X1,X2)|?[X3]:(in(X3,X1)&in(X3,X2)))&(![X3]:(~(in(X3,X1))|~(in(X3,X2)))|~(disjoint(X1,X2)))),inference(fof_nnf,[status(thm)],[66])). fof(216, plain,![X4]:![X5]:((disjoint(X4,X5)|?[X6]:(in(X6,X4)&in(X6,X5)))&(![X7]:(~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(variable_rename,[status(thm)],[215])). fof(217, plain,![X4]:![X5]:((disjoint(X4,X5)|(in(esk9_2(X4,X5),X4)&in(esk9_2(X4,X5),X5)))&(![X7]:(~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(skolemize,[status(esa)],[216])). fof(218, plain,![X4]:![X5]:![X7]:((disjoint(X4,X5)|(in(esk9_2(X4,X5),X4)&in(esk9_2(X4,X5),X5)))&((~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(shift_quantors,[status(thm)],[217])). fof(219, plain,![X4]:![X5]:![X7]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(distribute,[status(thm)],[218])). cnf(220,plain,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)),inference(split_conjunct,[status(thm)],[219])). cnf(221,plain,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)),inference(split_conjunct,[status(thm)],[219])). cnf(222,plain,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)),inference(split_conjunct,[status(thm)],[219])). fof(244, negated_conjecture,?[X1]:?[X2]:?[X3]:((subset(X1,X2)&disjoint(X2,X3))&~(disjoint(X1,X3))),inference(fof_nnf,[status(thm)],[57])). fof(245, negated_conjecture,?[X4]:?[X5]:?[X6]:((subset(X4,X5)&disjoint(X5,X6))&~(disjoint(X4,X6))),inference(variable_rename,[status(thm)],[244])). fof(246, negated_conjecture,((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~(disjoint(esk11_0,esk13_0))),inference(skolemize,[status(esa)],[245])). cnf(247,negated_conjecture,(~disjoint(esk11_0,esk13_0)),inference(split_conjunct,[status(thm)],[246])). cnf(248,negated_conjecture,(disjoint(esk12_0,esk13_0)),inference(split_conjunct,[status(thm)],[246])). cnf(249,negated_conjecture,(subset(esk11_0,esk12_0)),inference(split_conjunct,[status(thm)],[246])). cnf(384,plain,(disjoint(X1,X2)|in(esk9_2(X2,X1),X1)),inference(spm,[status(thm)],[172,221,theory(equality)])). cnf(386,plain,(disjoint(X1,X2)|in(esk9_2(X2,X1),X2)),inference(spm,[status(thm)],[172,222,theory(equality)])). cnf(474,negated_conjecture,(in(X1,esk12_0)|~in(X1,esk11_0)),inference(spm,[status(thm)],[108,249,theory(equality)])). cnf(485,negated_conjecture,(~in(X1,esk13_0)|~in(X1,esk12_0)),inference(spm,[status(thm)],[220,248,theory(equality)])). cnf(2151,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk11_0)),inference(spm,[status(thm)],[247,384,theory(equality)])). cnf(2160,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk13_0)),inference(spm,[status(thm)],[247,386,theory(equality)])). cnf(2169,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk12_0)),inference(spm,[status(thm)],[485,2160,theory(equality)])). cnf(2622,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk11_0)),inference(spm,[status(thm)],[2169,474,theory(equality)])). cnf(2640,negated_conjecture,($false),inference(rw,[status(thm)],[2622,2151,theory(equality)])). cnf(2641,negated_conjecture,($false),inference(cn,[status(thm)],[2640,theory(equality)])). cnf(2642,negated_conjecture,($false),2641,['proof']). # SZS output end CNFRefutation
# Preprocessing time : 0.010 s # Problem is satisfiable (or invalid), generating saturation derivation # SZS status CounterSatisfiable # SZS output start Saturation. fof(1, axiom,![X1]:![X2]:(woman(X1,X2)=>female(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax1)). fof(2, axiom,![X1]:![X2]:(human_person(X1,X2)=>animate(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax2)). fof(3, axiom,![X1]:![X2]:(human_person(X1,X2)=>human(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax3)). fof(4, axiom,![X1]:![X2]:(organism(X1,X2)=>living(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax4)). fof(5, axiom,![X1]:![X2]:(organism(X1,X2)=>impartial(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax5)). fof(6, axiom,![X1]:![X2]:(organism(X1,X2)=>entity(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax6)). fof(7, axiom,![X1]:![X2]:(human_person(X1,X2)=>organism(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax7)). fof(8, axiom,![X1]:![X2]:(woman(X1,X2)=>human_person(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax8)). fof(9, axiom,![X1]:![X2]:(mia_forename(X1,X2)=>forename(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax9)). fof(10, axiom,![X1]:![X2]:(abstraction(X1,X2)=>unisex(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax10)). fof(11, axiom,![X1]:![X2]:(abstraction(X1,X2)=>general(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax11)). fof(12, axiom,![X1]:![X2]:(abstraction(X1,X2)=>nonhuman(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax12)). fof(13, axiom,![X1]:![X2]:(abstraction(X1,X2)=>thing(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax13)). fof(14, axiom,![X1]:![X2]:(relation(X1,X2)=>abstraction(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax14)). fof(15, axiom,![X1]:![X2]:(relname(X1,X2)=>relation(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax15)). fof(16, axiom,![X1]:![X2]:(forename(X1,X2)=>relname(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax16)). fof(17, axiom,![X1]:![X2]:(object(X1,X2)=>unisex(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax17)). fof(18, axiom,![X1]:![X2]:(object(X1,X2)=>impartial(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax18)). fof(19, axiom,![X1]:![X2]:(object(X1,X2)=>nonliving(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax19)). fof(20, axiom,![X1]:![X2]:(entity(X1,X2)=>existent(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax20)). fof(21, axiom,![X1]:![X2]:(entity(X1,X2)=>specific(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax21)). fof(22, axiom,![X1]:![X2]:(entity(X1,X2)=>thing(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax22)). fof(23, axiom,![X1]:![X2]:(object(X1,X2)=>entity(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax23)). fof(24, axiom,![X1]:![X2]:(substance_matter(X1,X2)=>object(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax24)). fof(25, axiom,![X1]:![X2]:(food(X1,X2)=>substance_matter(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax25)). fof(26, axiom,![X1]:![X2]:(beverage(X1,X2)=>food(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax26)). fof(27, axiom,![X1]:![X2]:(shake_beverage(X1,X2)=>beverage(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax27)). fof(28, axiom,![X1]:![X2]:(order(X1,X2)=>event(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax28)). fof(29, axiom,![X1]:![X2]:(eventuality(X1,X2)=>unisex(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax29)). fof(30, axiom,![X1]:![X2]:(eventuality(X1,X2)=>nonexistent(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax30)). fof(31, axiom,![X1]:![X2]:(eventuality(X1,X2)=>specific(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax31)). fof(32, axiom,![X1]:![X2]:(thing(X1,X2)=>singleton(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax32)). fof(33, axiom,![X1]:![X2]:(eventuality(X1,X2)=>thing(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax33)). fof(34, axiom,![X1]:![X2]:(event(X1,X2)=>eventuality(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax34)). fof(35, axiom,![X1]:![X2]:(act(X1,X2)=>event(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax35)). fof(36, axiom,![X1]:![X2]:(order(X1,X2)=>act(X1,X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax36)). fof(37, axiom,![X1]:![X2]:(animate(X1,X2)=>~(nonliving(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax37)). fof(38, axiom,![X1]:![X2]:(existent(X1,X2)=>~(nonexistent(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax38)). fof(39, axiom,![X1]:![X2]:(nonhuman(X1,X2)=>~(human(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax39)). fof(40, axiom,![X1]:![X2]:(nonliving(X1,X2)=>~(living(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax40)). fof(41, axiom,![X1]:![X2]:(specific(X1,X2)=>~(general(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax41)). fof(42, axiom,![X1]:![X2]:(unisex(X1,X2)=>~(female(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax42)). fof(43, axiom,![X1]:![X2]:![X3]:(((entity(X1,X2)&forename(X1,X3))&of(X1,X3,X2))=>~(?[X4]:((forename(X1,X4)&~(X4=X3))&of(X1,X4,X2)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax43)). fof(44, axiom,![X1]:![X2]:![X3]:![X4]:(((nonreflexive(X1,X2)&agent(X1,X2,X3))&patient(X1,X2,X4))=>~(X3=X4)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', ax44)). fof(45, conjecture,~(?[X1]:(actual_world(X1)&?[X2]:?[X3]:?[X4]:?[X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/NLP042+1.p', co1)). fof(46, negated_conjecture,~(~(?[X1]:(actual_world(X1)&?[X2]:?[X3]:?[X4]:?[X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5))))),inference(assume_negation,[status(cth)],[45])). fof(47, plain,![X1]:![X2]:(animate(X1,X2)=>~(nonliving(X1,X2))),inference(fof_simplification,[status(thm)],[37,theory(equality)])). fof(48, plain,![X1]:![X2]:(existent(X1,X2)=>~(nonexistent(X1,X2))),inference(fof_simplification,[status(thm)],[38,theory(equality)])). fof(49, plain,![X1]:![X2]:(nonhuman(X1,X2)=>~(human(X1,X2))),inference(fof_simplification,[status(thm)],[39,theory(equality)])). fof(50, plain,![X1]:![X2]:(nonliving(X1,X2)=>~(living(X1,X2))),inference(fof_simplification,[status(thm)],[40,theory(equality)])). fof(51, plain,![X1]:![X2]:(specific(X1,X2)=>~(general(X1,X2))),inference(fof_simplification,[status(thm)],[41,theory(equality)])). fof(52, plain,![X1]:![X2]:(unisex(X1,X2)=>~(female(X1,X2))),inference(fof_simplification,[status(thm)],[42,theory(equality)])). fof(53, plain,![X1]:![X2]:(~(woman(X1,X2))|female(X1,X2)),inference(fof_nnf,[status(thm)],[1])). fof(54, plain,![X3]:![X4]:(~(woman(X3,X4))|female(X3,X4)),inference(variable_rename,[status(thm)],[53])). cnf(55,plain,(female(X1,X2)|~woman(X1,X2)),inference(split_conjunct,[status(thm)],[54])). fof(56, plain,![X1]:![X2]:(~(human_person(X1,X2))|animate(X1,X2)),inference(fof_nnf,[status(thm)],[2])). fof(57, plain,![X3]:![X4]:(~(human_person(X3,X4))|animate(X3,X4)),inference(variable_rename,[status(thm)],[56])). cnf(58,plain,(animate(X1,X2)|~human_person(X1,X2)),inference(split_conjunct,[status(thm)],[57])). fof(59, plain,![X1]:![X2]:(~(human_person(X1,X2))|human(X1,X2)),inference(fof_nnf,[status(thm)],[3])). fof(60, plain,![X3]:![X4]:(~(human_person(X3,X4))|human(X3,X4)),inference(variable_rename,[status(thm)],[59])). cnf(61,plain,(human(X1,X2)|~human_person(X1,X2)),inference(split_conjunct,[status(thm)],[60])). fof(62, plain,![X1]:![X2]:(~(organism(X1,X2))|living(X1,X2)),inference(fof_nnf,[status(thm)],[4])). fof(63, plain,![X3]:![X4]:(~(organism(X3,X4))|living(X3,X4)),inference(variable_rename,[status(thm)],[62])). cnf(64,plain,(living(X1,X2)|~organism(X1,X2)),inference(split_conjunct,[status(thm)],[63])). fof(65, plain,![X1]:![X2]:(~(organism(X1,X2))|impartial(X1,X2)),inference(fof_nnf,[status(thm)],[5])). fof(66, plain,![X3]:![X4]:(~(organism(X3,X4))|impartial(X3,X4)),inference(variable_rename,[status(thm)],[65])). cnf(67,plain,(impartial(X1,X2)|~organism(X1,X2)),inference(split_conjunct,[status(thm)],[66])). fof(68, plain,![X1]:![X2]:(~(organism(X1,X2))|entity(X1,X2)),inference(fof_nnf,[status(thm)],[6])). fof(69, plain,![X3]:![X4]:(~(organism(X3,X4))|entity(X3,X4)),inference(variable_rename,[status(thm)],[68])). cnf(70,plain,(entity(X1,X2)|~organism(X1,X2)),inference(split_conjunct,[status(thm)],[69])). fof(71, plain,![X1]:![X2]:(~(human_person(X1,X2))|organism(X1,X2)),inference(fof_nnf,[status(thm)],[7])). fof(72, plain,![X3]:![X4]:(~(human_person(X3,X4))|organism(X3,X4)),inference(variable_rename,[status(thm)],[71])). cnf(73,plain,(organism(X1,X2)|~human_person(X1,X2)),inference(split_conjunct,[status(thm)],[72])). fof(74, plain,![X1]:![X2]:(~(woman(X1,X2))|human_person(X1,X2)),inference(fof_nnf,[status(thm)],[8])). fof(75, plain,![X3]:![X4]:(~(woman(X3,X4))|human_person(X3,X4)),inference(variable_rename,[status(thm)],[74])). cnf(76,plain,(human_person(X1,X2)|~woman(X1,X2)),inference(split_conjunct,[status(thm)],[75])). fof(77, plain,![X1]:![X2]:(~(mia_forename(X1,X2))|forename(X1,X2)),inference(fof_nnf,[status(thm)],[9])). fof(78, plain,![X3]:![X4]:(~(mia_forename(X3,X4))|forename(X3,X4)),inference(variable_rename,[status(thm)],[77])). cnf(79,plain,(forename(X1,X2)|~mia_forename(X1,X2)),inference(split_conjunct,[status(thm)],[78])). fof(80, plain,![X1]:![X2]:(~(abstraction(X1,X2))|unisex(X1,X2)),inference(fof_nnf,[status(thm)],[10])). fof(81, plain,![X3]:![X4]:(~(abstraction(X3,X4))|unisex(X3,X4)),inference(variable_rename,[status(thm)],[80])). cnf(82,plain,(unisex(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[81])). fof(83, plain,![X1]:![X2]:(~(abstraction(X1,X2))|general(X1,X2)),inference(fof_nnf,[status(thm)],[11])). fof(84, plain,![X3]:![X4]:(~(abstraction(X3,X4))|general(X3,X4)),inference(variable_rename,[status(thm)],[83])). cnf(85,plain,(general(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[84])). fof(86, plain,![X1]:![X2]:(~(abstraction(X1,X2))|nonhuman(X1,X2)),inference(fof_nnf,[status(thm)],[12])). fof(87, plain,![X3]:![X4]:(~(abstraction(X3,X4))|nonhuman(X3,X4)),inference(variable_rename,[status(thm)],[86])). cnf(88,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[87])). fof(89, plain,![X1]:![X2]:(~(abstraction(X1,X2))|thing(X1,X2)),inference(fof_nnf,[status(thm)],[13])). fof(90, plain,![X3]:![X4]:(~(abstraction(X3,X4))|thing(X3,X4)),inference(variable_rename,[status(thm)],[89])). cnf(91,plain,(thing(X1,X2)|~abstraction(X1,X2)),inference(split_conjunct,[status(thm)],[90])). fof(92, plain,![X1]:![X2]:(~(relation(X1,X2))|abstraction(X1,X2)),inference(fof_nnf,[status(thm)],[14])). fof(93, plain,![X3]:![X4]:(~(relation(X3,X4))|abstraction(X3,X4)),inference(variable_rename,[status(thm)],[92])). cnf(94,plain,(abstraction(X1,X2)|~relation(X1,X2)),inference(split_conjunct,[status(thm)],[93])). fof(95, plain,![X1]:![X2]:(~(relname(X1,X2))|relation(X1,X2)),inference(fof_nnf,[status(thm)],[15])). fof(96, plain,![X3]:![X4]:(~(relname(X3,X4))|relation(X3,X4)),inference(variable_rename,[status(thm)],[95])). cnf(97,plain,(relation(X1,X2)|~relname(X1,X2)),inference(split_conjunct,[status(thm)],[96])). fof(98, plain,![X1]:![X2]:(~(forename(X1,X2))|relname(X1,X2)),inference(fof_nnf,[status(thm)],[16])). fof(99, plain,![X3]:![X4]:(~(forename(X3,X4))|relname(X3,X4)),inference(variable_rename,[status(thm)],[98])). cnf(100,plain,(relname(X1,X2)|~forename(X1,X2)),inference(split_conjunct,[status(thm)],[99])). fof(101, plain,![X1]:![X2]:(~(object(X1,X2))|unisex(X1,X2)),inference(fof_nnf,[status(thm)],[17])). fof(102, plain,![X3]:![X4]:(~(object(X3,X4))|unisex(X3,X4)),inference(variable_rename,[status(thm)],[101])). cnf(103,plain,(unisex(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[102])). fof(104, plain,![X1]:![X2]:(~(object(X1,X2))|impartial(X1,X2)),inference(fof_nnf,[status(thm)],[18])). fof(105, plain,![X3]:![X4]:(~(object(X3,X4))|impartial(X3,X4)),inference(variable_rename,[status(thm)],[104])). cnf(106,plain,(impartial(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[105])). fof(107, plain,![X1]:![X2]:(~(object(X1,X2))|nonliving(X1,X2)),inference(fof_nnf,[status(thm)],[19])). fof(108, plain,![X3]:![X4]:(~(object(X3,X4))|nonliving(X3,X4)),inference(variable_rename,[status(thm)],[107])). cnf(109,plain,(nonliving(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[108])). fof(110, plain,![X1]:![X2]:(~(entity(X1,X2))|existent(X1,X2)),inference(fof_nnf,[status(thm)],[20])). fof(111, plain,![X3]:![X4]:(~(entity(X3,X4))|existent(X3,X4)),inference(variable_rename,[status(thm)],[110])). cnf(112,plain,(existent(X1,X2)|~entity(X1,X2)),inference(split_conjunct,[status(thm)],[111])). fof(113, plain,![X1]:![X2]:(~(entity(X1,X2))|specific(X1,X2)),inference(fof_nnf,[status(thm)],[21])). fof(114, plain,![X3]:![X4]:(~(entity(X3,X4))|specific(X3,X4)),inference(variable_rename,[status(thm)],[113])). cnf(115,plain,(specific(X1,X2)|~entity(X1,X2)),inference(split_conjunct,[status(thm)],[114])). fof(116, plain,![X1]:![X2]:(~(entity(X1,X2))|thing(X1,X2)),inference(fof_nnf,[status(thm)],[22])). fof(117, plain,![X3]:![X4]:(~(entity(X3,X4))|thing(X3,X4)),inference(variable_rename,[status(thm)],[116])). cnf(118,plain,(thing(X1,X2)|~entity(X1,X2)),inference(split_conjunct,[status(thm)],[117])). fof(119, plain,![X1]:![X2]:(~(object(X1,X2))|entity(X1,X2)),inference(fof_nnf,[status(thm)],[23])). fof(120, plain,![X3]:![X4]:(~(object(X3,X4))|entity(X3,X4)),inference(variable_rename,[status(thm)],[119])). cnf(121,plain,(entity(X1,X2)|~object(X1,X2)),inference(split_conjunct,[status(thm)],[120])). fof(122, plain,![X1]:![X2]:(~(substance_matter(X1,X2))|object(X1,X2)),inference(fof_nnf,[status(thm)],[24])). fof(123, plain,![X3]:![X4]:(~(substance_matter(X3,X4))|object(X3,X4)),inference(variable_rename,[status(thm)],[122])). cnf(124,plain,(object(X1,X2)|~substance_matter(X1,X2)),inference(split_conjunct,[status(thm)],[123])). fof(125, plain,![X1]:![X2]:(~(food(X1,X2))|substance_matter(X1,X2)),inference(fof_nnf,[status(thm)],[25])). fof(126, plain,![X3]:![X4]:(~(food(X3,X4))|substance_matter(X3,X4)),inference(variable_rename,[status(thm)],[125])). cnf(127,plain,(substance_matter(X1,X2)|~food(X1,X2)),inference(split_conjunct,[status(thm)],[126])). fof(128, plain,![X1]:![X2]:(~(beverage(X1,X2))|food(X1,X2)),inference(fof_nnf,[status(thm)],[26])). fof(129, plain,![X3]:![X4]:(~(beverage(X3,X4))|food(X3,X4)),inference(variable_rename,[status(thm)],[128])). cnf(130,plain,(food(X1,X2)|~beverage(X1,X2)),inference(split_conjunct,[status(thm)],[129])). fof(131, plain,![X1]:![X2]:(~(shake_beverage(X1,X2))|beverage(X1,X2)),inference(fof_nnf,[status(thm)],[27])). fof(132, plain,![X3]:![X4]:(~(shake_beverage(X3,X4))|beverage(X3,X4)),inference(variable_rename,[status(thm)],[131])). cnf(133,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)),inference(split_conjunct,[status(thm)],[132])). fof(134, plain,![X1]:![X2]:(~(order(X1,X2))|event(X1,X2)),inference(fof_nnf,[status(thm)],[28])). fof(135, plain,![X3]:![X4]:(~(order(X3,X4))|event(X3,X4)),inference(variable_rename,[status(thm)],[134])). cnf(136,plain,(event(X1,X2)|~order(X1,X2)),inference(split_conjunct,[status(thm)],[135])). fof(137, plain,![X1]:![X2]:(~(eventuality(X1,X2))|unisex(X1,X2)),inference(fof_nnf,[status(thm)],[29])). fof(138, plain,![X3]:![X4]:(~(eventuality(X3,X4))|unisex(X3,X4)),inference(variable_rename,[status(thm)],[137])). cnf(139,plain,(unisex(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[138])). fof(140, plain,![X1]:![X2]:(~(eventuality(X1,X2))|nonexistent(X1,X2)),inference(fof_nnf,[status(thm)],[30])). fof(141, plain,![X3]:![X4]:(~(eventuality(X3,X4))|nonexistent(X3,X4)),inference(variable_rename,[status(thm)],[140])). cnf(142,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[141])). fof(143, plain,![X1]:![X2]:(~(eventuality(X1,X2))|specific(X1,X2)),inference(fof_nnf,[status(thm)],[31])). fof(144, plain,![X3]:![X4]:(~(eventuality(X3,X4))|specific(X3,X4)),inference(variable_rename,[status(thm)],[143])). cnf(145,plain,(specific(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[144])). fof(146, plain,![X1]:![X2]:(~(thing(X1,X2))|singleton(X1,X2)),inference(fof_nnf,[status(thm)],[32])). fof(147, plain,![X3]:![X4]:(~(thing(X3,X4))|singleton(X3,X4)),inference(variable_rename,[status(thm)],[146])). cnf(148,plain,(singleton(X1,X2)|~thing(X1,X2)),inference(split_conjunct,[status(thm)],[147])). fof(149, plain,![X1]:![X2]:(~(eventuality(X1,X2))|thing(X1,X2)),inference(fof_nnf,[status(thm)],[33])). fof(150, plain,![X3]:![X4]:(~(eventuality(X3,X4))|thing(X3,X4)),inference(variable_rename,[status(thm)],[149])). cnf(151,plain,(thing(X1,X2)|~eventuality(X1,X2)),inference(split_conjunct,[status(thm)],[150])). fof(152, plain,![X1]:![X2]:(~(event(X1,X2))|eventuality(X1,X2)),inference(fof_nnf,[status(thm)],[34])). fof(153, plain,![X3]:![X4]:(~(event(X3,X4))|eventuality(X3,X4)),inference(variable_rename,[status(thm)],[152])). cnf(154,plain,(eventuality(X1,X2)|~event(X1,X2)),inference(split_conjunct,[status(thm)],[153])). fof(155, plain,![X1]:![X2]:(~(act(X1,X2))|event(X1,X2)),inference(fof_nnf,[status(thm)],[35])). fof(156, plain,![X3]:![X4]:(~(act(X3,X4))|event(X3,X4)),inference(variable_rename,[status(thm)],[155])). cnf(157,plain,(event(X1,X2)|~act(X1,X2)),inference(split_conjunct,[status(thm)],[156])). fof(158, plain,![X1]:![X2]:(~(order(X1,X2))|act(X1,X2)),inference(fof_nnf,[status(thm)],[36])). fof(159, plain,![X3]:![X4]:(~(order(X3,X4))|act(X3,X4)),inference(variable_rename,[status(thm)],[158])). cnf(160,plain,(act(X1,X2)|~order(X1,X2)),inference(split_conjunct,[status(thm)],[159])). fof(161, plain,![X1]:![X2]:(~(animate(X1,X2))|~(nonliving(X1,X2))),inference(fof_nnf,[status(thm)],[47])). fof(162, plain,![X3]:![X4]:(~(animate(X3,X4))|~(nonliving(X3,X4))),inference(variable_rename,[status(thm)],[161])). cnf(163,plain,(~nonliving(X1,X2)|~animate(X1,X2)),inference(split_conjunct,[status(thm)],[162])). fof(164, plain,![X1]:![X2]:(~(existent(X1,X2))|~(nonexistent(X1,X2))),inference(fof_nnf,[status(thm)],[48])). fof(165, plain,![X3]:![X4]:(~(existent(X3,X4))|~(nonexistent(X3,X4))),inference(variable_rename,[status(thm)],[164])). cnf(166,plain,(~nonexistent(X1,X2)|~existent(X1,X2)),inference(split_conjunct,[status(thm)],[165])). fof(167, plain,![X1]:![X2]:(~(nonhuman(X1,X2))|~(human(X1,X2))),inference(fof_nnf,[status(thm)],[49])). fof(168, plain,![X3]:![X4]:(~(nonhuman(X3,X4))|~(human(X3,X4))),inference(variable_rename,[status(thm)],[167])). cnf(169,plain,(~human(X1,X2)|~nonhuman(X1,X2)),inference(split_conjunct,[status(thm)],[168])). fof(170, plain,![X1]:![X2]:(~(nonliving(X1,X2))|~(living(X1,X2))),inference(fof_nnf,[status(thm)],[50])). fof(171, plain,![X3]:![X4]:(~(nonliving(X3,X4))|~(living(X3,X4))),inference(variable_rename,[status(thm)],[170])). cnf(172,plain,(~living(X1,X2)|~nonliving(X1,X2)),inference(split_conjunct,[status(thm)],[171])). fof(173, plain,![X1]:![X2]:(~(specific(X1,X2))|~(general(X1,X2))),inference(fof_nnf,[status(thm)],[51])). fof(174, plain,![X3]:![X4]:(~(specific(X3,X4))|~(general(X3,X4))),inference(variable_rename,[status(thm)],[173])). cnf(175,plain,(~general(X1,X2)|~specific(X1,X2)),inference(split_conjunct,[status(thm)],[174])). fof(176, plain,![X1]:![X2]:(~(unisex(X1,X2))|~(female(X1,X2))),inference(fof_nnf,[status(thm)],[52])). fof(177, plain,![X3]:![X4]:(~(unisex(X3,X4))|~(female(X3,X4))),inference(variable_rename,[status(thm)],[176])). cnf(178,plain,(~female(X1,X2)|~unisex(X1,X2)),inference(split_conjunct,[status(thm)],[177])). fof(179, plain,![X1]:![X2]:![X3]:(((~(entity(X1,X2))|~(forename(X1,X3)))|~(of(X1,X3,X2)))|![X4]:((~(forename(X1,X4))|X4=X3)|~(of(X1,X4,X2)))),inference(fof_nnf,[status(thm)],[43])). fof(180, plain,![X5]:![X6]:![X7]:(((~(entity(X5,X6))|~(forename(X5,X7)))|~(of(X5,X7,X6)))|![X8]:((~(forename(X5,X8))|X8=X7)|~(of(X5,X8,X6)))),inference(variable_rename,[status(thm)],[179])). fof(181, plain,![X5]:![X6]:![X7]:![X8]:(((~(entity(X5,X6))|~(forename(X5,X7)))|~(of(X5,X7,X6)))|((~(forename(X5,X8))|X8=X7)|~(of(X5,X8,X6)))),inference(shift_quantors,[status(thm)],[180])). cnf(182,plain,(X2=X4|~of(X1,X2,X3)|~forename(X1,X2)|~of(X1,X4,X3)|~forename(X1,X4)|~entity(X1,X3)),inference(split_conjunct,[status(thm)],[181])). fof(183, plain,![X1]:![X2]:![X3]:![X4]:(((~(nonreflexive(X1,X2))|~(agent(X1,X2,X3)))|~(patient(X1,X2,X4)))|~(X3=X4)),inference(fof_nnf,[status(thm)],[44])). fof(184, plain,![X5]:![X6]:![X7]:![X8]:(((~(nonreflexive(X5,X6))|~(agent(X5,X6,X7)))|~(patient(X5,X6,X8)))|~(X7=X8)),inference(variable_rename,[status(thm)],[183])). cnf(185,plain,(X1!=X2|~patient(X3,X4,X2)|~agent(X3,X4,X1)|~nonreflexive(X3,X4)),inference(split_conjunct,[status(thm)],[184])). fof(186, negated_conjecture,?[X1]:(actual_world(X1)&?[X2]:?[X3]:?[X4]:?[X5]:((((((((((of(X1,X3,X2)&woman(X1,X2))&mia_forename(X1,X3))&forename(X1,X3))&shake_beverage(X1,X4))&event(X1,X5))&agent(X1,X5,X2))&patient(X1,X5,X4))&past(X1,X5))&nonreflexive(X1,X5))&order(X1,X5))),inference(fof_nnf,[status(thm)],[46])). fof(187, negated_conjecture,?[X6]:(actual_world(X6)&?[X7]:?[X8]:?[X9]:?[X10]:((((((((((of(X6,X8,X7)&woman(X6,X7))&mia_forename(X6,X8))&forename(X6,X8))&shake_beverage(X6,X9))&event(X6,X10))&agent(X6,X10,X7))&patient(X6,X10,X9))&past(X6,X10))&nonreflexive(X6,X10))&order(X6,X10))),inference(variable_rename,[status(thm)],[186])). fof(188, negated_conjecture,(actual_world(esk1_0)&((((((((((of(esk1_0,esk3_0,esk2_0)&woman(esk1_0,esk2_0))&mia_forename(esk1_0,esk3_0))&forename(esk1_0,esk3_0))&shake_beverage(esk1_0,esk4_0))&event(esk1_0,esk5_0))&agent(esk1_0,esk5_0,esk2_0))&patient(esk1_0,esk5_0,esk4_0))&past(esk1_0,esk5_0))&nonreflexive(esk1_0,esk5_0))&order(esk1_0,esk5_0))),inference(skolemize,[status(esa)],[187])). cnf(189,negated_conjecture,(order(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])). cnf(190,negated_conjecture,(nonreflexive(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])). cnf(191,negated_conjecture,(past(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])). cnf(192,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)),inference(split_conjunct,[status(thm)],[188])). cnf(193,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)),inference(split_conjunct,[status(thm)],[188])). cnf(194,negated_conjecture,(event(esk1_0,esk5_0)),inference(split_conjunct,[status(thm)],[188])). cnf(195,negated_conjecture,(shake_beverage(esk1_0,esk4_0)),inference(split_conjunct,[status(thm)],[188])). cnf(196,negated_conjecture,(forename(esk1_0,esk3_0)),inference(split_conjunct,[status(thm)],[188])). cnf(197,negated_conjecture,(mia_forename(esk1_0,esk3_0)),inference(split_conjunct,[status(thm)],[188])). cnf(198,negated_conjecture,(woman(esk1_0,esk2_0)),inference(split_conjunct,[status(thm)],[188])). cnf(199,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)),inference(split_conjunct,[status(thm)],[188])). cnf(200,negated_conjecture,(actual_world(esk1_0)),inference(split_conjunct,[status(thm)],[188])). cnf(201,plain,(~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)),inference(er,[status(thm)],[185,theory(equality)])). cnf(206,negated_conjecture,(human_person(esk1_0,esk2_0)),inference(spm,[status(thm)],[76,198,theory(equality)])). cnf(207,negated_conjecture,(eventuality(esk1_0,esk5_0)),inference(spm,[status(thm)],[154,194,theory(equality)])). cnf(209,plain,(relation(X1,X2)|~forename(X1,X2)),inference(spm,[status(thm)],[97,100,theory(equality)])). cnf(210,plain,(food(X1,X2)|~shake_beverage(X1,X2)),inference(spm,[status(thm)],[130,133,theory(equality)])). cnf(211,plain,(~unisex(X1,X2)|~woman(X1,X2)),inference(spm,[status(thm)],[178,55,theory(equality)])). cnf(212,plain,(entity(X1,X2)|~human_person(X1,X2)),inference(spm,[status(thm)],[70,73,theory(equality)])). cnf(213,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)|~nonreflexive(esk1_0,esk5_0)),inference(spm,[status(thm)],[201,192,theory(equality)])). cnf(214,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)|$false),inference(rw,[status(thm)],[213,190,theory(equality)])). cnf(215,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)),inference(cn,[status(thm)],[214,theory(equality)])). cnf(216,plain,(~existent(X1,X2)|~eventuality(X1,X2)),inference(spm,[status(thm)],[166,142,theory(equality)])). cnf(217,plain,(~nonliving(X1,X2)|~human_person(X1,X2)),inference(spm,[status(thm)],[163,58,theory(equality)])). cnf(218,plain,(~human(X1,X2)|~abstraction(X1,X2)),inference(spm,[status(thm)],[169,88,theory(equality)])). cnf(219,plain,(~specific(X1,X2)|~abstraction(X1,X2)),inference(spm,[status(thm)],[175,85,theory(equality)])). cnf(220,plain,(~nonliving(X1,X2)|~organism(X1,X2)),inference(spm,[status(thm)],[172,64,theory(equality)])). cnf(221,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,esk3_0)|~forename(esk1_0,X1)|~entity(esk1_0,esk2_0)),inference(spm,[status(thm)],[182,199,theory(equality)])). cnf(222,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|$false|~forename(esk1_0,X1)|~entity(esk1_0,esk2_0)),inference(rw,[status(thm)],[221,196,theory(equality)])). cnf(223,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)|~entity(esk1_0,esk2_0)),inference(cn,[status(thm)],[222,theory(equality)])). cnf(224,negated_conjecture,(~unisex(esk1_0,esk2_0)),inference(spm,[status(thm)],[211,198,theory(equality)])). cnf(225,negated_conjecture,(~abstraction(esk1_0,esk2_0)),inference(spm,[status(thm)],[224,82,theory(equality)])). cnf(226,negated_conjecture,(~object(esk1_0,esk2_0)),inference(spm,[status(thm)],[224,103,theory(equality)])). cnf(227,negated_conjecture,(~eventuality(esk1_0,esk2_0)),inference(spm,[status(thm)],[224,139,theory(equality)])). cnf(228,plain,(abstraction(X1,X2)|~forename(X1,X2)),inference(spm,[status(thm)],[94,209,theory(equality)])). cnf(229,plain,(substance_matter(X1,X2)|~shake_beverage(X1,X2)),inference(spm,[status(thm)],[127,210,theory(equality)])). cnf(230,negated_conjecture,(~forename(esk1_0,esk2_0)),inference(spm,[status(thm)],[225,228,theory(equality)])). cnf(231,negated_conjecture,(entity(esk1_0,esk2_0)),inference(spm,[status(thm)],[212,206,theory(equality)])). cnf(232,plain,(~eventuality(X1,X2)|~entity(X1,X2)),inference(spm,[status(thm)],[216,112,theory(equality)])). cnf(233,negated_conjecture,(~entity(esk1_0,esk5_0)),inference(spm,[status(thm)],[232,207,theory(equality)])). cnf(234,plain,(object(X1,X2)|~shake_beverage(X1,X2)),inference(spm,[status(thm)],[124,229,theory(equality)])). cnf(235,negated_conjecture,(object(esk1_0,esk4_0)),inference(spm,[status(thm)],[234,195,theory(equality)])). cnf(236,negated_conjecture,(entity(esk1_0,esk4_0)),inference(spm,[status(thm)],[121,235,theory(equality)])). cnf(237,plain,(~human_person(X1,X2)|~object(X1,X2)),inference(spm,[status(thm)],[217,109,theory(equality)])). cnf(239,plain,(~abstraction(X1,X2)|~human_person(X1,X2)),inference(spm,[status(thm)],[218,61,theory(equality)])). cnf(241,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)|$false),inference(rw,[status(thm)],[223,231,theory(equality)])). cnf(242,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)),inference(cn,[status(thm)],[241,theory(equality)])). cnf(243,plain,(~abstraction(X1,X2)|~entity(X1,X2)),inference(spm,[status(thm)],[219,115,theory(equality)])). cnf(244,plain,(~abstraction(X1,X2)|~eventuality(X1,X2)),inference(spm,[status(thm)],[219,145,theory(equality)])). cnf(245,plain,(~organism(X1,X2)|~object(X1,X2)),inference(spm,[status(thm)],[220,109,theory(equality)])). cnf(246,negated_conjecture,(~abstraction(esk1_0,esk5_0)),inference(spm,[status(thm)],[244,207,theory(equality)])). cnf(247,negated_conjecture,(~forename(esk1_0,esk5_0)),inference(spm,[status(thm)],[246,228,theory(equality)])). cnf(249,plain,(~entity(X1,X2)|~forename(X1,X2)),inference(spm,[status(thm)],[243,228,theory(equality)])). cnf(250,negated_conjecture,(~entity(esk1_0,esk3_0)),inference(spm,[status(thm)],[249,196,theory(equality)])). cnf(251,negated_conjecture,(actual_world(esk1_0)),200,['final']). cnf(252,negated_conjecture,(woman(esk1_0,esk2_0)),198,['final']). cnf(253,negated_conjecture,(mia_forename(esk1_0,esk3_0)),197,['final']). cnf(254,negated_conjecture,(forename(esk1_0,esk3_0)),196,['final']). cnf(255,negated_conjecture,(shake_beverage(esk1_0,esk4_0)),195,['final']). cnf(256,negated_conjecture,(order(esk1_0,esk5_0)),189,['final']). cnf(257,negated_conjecture,(event(esk1_0,esk5_0)),194,['final']). cnf(258,negated_conjecture,(nonreflexive(esk1_0,esk5_0)),190,['final']). cnf(259,negated_conjecture,(past(esk1_0,esk5_0)),191,['final']). cnf(260,negated_conjecture,(of(esk1_0,esk3_0,esk2_0)),199,['final']). cnf(261,negated_conjecture,(agent(esk1_0,esk5_0,esk2_0)),193,['final']). cnf(262,negated_conjecture,(patient(esk1_0,esk5_0,esk4_0)),192,['final']). cnf(263,negated_conjecture,(human_person(esk1_0,esk2_0)),206,['final']). cnf(264,negated_conjecture,(eventuality(esk1_0,esk5_0)),207,['final']). cnf(265,negated_conjecture,(entity(esk1_0,esk2_0)),231,['final']). cnf(266,negated_conjecture,(object(esk1_0,esk4_0)),235,['final']). cnf(267,negated_conjecture,(entity(esk1_0,esk4_0)),236,['final']). cnf(268,negated_conjecture,(~agent(esk1_0,esk5_0,esk4_0)),215,['final']). cnf(269,negated_conjecture,(~unisex(esk1_0,esk2_0)),224,['final']). cnf(270,negated_conjecture,(~eventuality(esk1_0,esk2_0)),227,['final']). cnf(271,negated_conjecture,(~object(esk1_0,esk2_0)),226,['final']). cnf(272,negated_conjecture,(~abstraction(esk1_0,esk2_0)),225,['final']). cnf(273,negated_conjecture,(~forename(esk1_0,esk2_0)),230,['final']). cnf(274,negated_conjecture,(~entity(esk1_0,esk5_0)),233,['final']). cnf(275,negated_conjecture,(~abstraction(esk1_0,esk5_0)),246,['final']). cnf(276,negated_conjecture,(~forename(esk1_0,esk5_0)),247,['final']). cnf(277,negated_conjecture,(~entity(esk1_0,esk3_0)),250,['final']). cnf(278,plain,(forename(X1,X2)|~mia_forename(X1,X2)),79,['final']). cnf(279,plain,(event(X1,X2)|~order(X1,X2)),136,['final']). cnf(280,plain,(human_person(X1,X2)|~woman(X1,X2)),76,['final']). cnf(281,plain,(eventuality(X1,X2)|~event(X1,X2)),154,['final']). cnf(282,plain,(female(X1,X2)|~woman(X1,X2)),55,['final']). cnf(283,plain,(relname(X1,X2)|~forename(X1,X2)),100,['final']). cnf(284,plain,(beverage(X1,X2)|~shake_beverage(X1,X2)),133,['final']). cnf(285,plain,(event(X1,X2)|~act(X1,X2)),157,['final']). cnf(286,plain,(act(X1,X2)|~order(X1,X2)),160,['final']). cnf(287,plain,(animate(X1,X2)|~human_person(X1,X2)),58,['final']). cnf(288,plain,(human(X1,X2)|~human_person(X1,X2)),61,['final']). cnf(289,plain,(organism(X1,X2)|~human_person(X1,X2)),73,['final']). cnf(290,plain,(relation(X1,X2)|~relname(X1,X2)),97,['final']). cnf(291,plain,(food(X1,X2)|~beverage(X1,X2)),130,['final']). cnf(292,plain,(~unisex(X1,X2)|~female(X1,X2)),178,['final']). cnf(293,plain,(entity(X1,X2)|~organism(X1,X2)),70,['final']). cnf(294,plain,(living(X1,X2)|~organism(X1,X2)),64,['final']). cnf(295,plain,(impartial(X1,X2)|~organism(X1,X2)),67,['final']). cnf(296,plain,(impartial(X1,X2)|~object(X1,X2)),106,['final']). cnf(297,plain,(entity(X1,X2)|~object(X1,X2)),121,['final']). cnf(298,plain,(abstraction(X1,X2)|~relation(X1,X2)),94,['final']). cnf(299,plain,(unisex(X1,X2)|~eventuality(X1,X2)),139,['final']). cnf(300,plain,(thing(X1,X2)|~entity(X1,X2)),118,['final']). cnf(301,plain,(thing(X1,X2)|~eventuality(X1,X2)),151,['final']). cnf(302,plain,(existent(X1,X2)|~entity(X1,X2)),112,['final']). cnf(303,plain,(unisex(X1,X2)|~abstraction(X1,X2)),82,['final']). cnf(304,plain,(unisex(X1,X2)|~object(X1,X2)),103,['final']). cnf(305,plain,(specific(X1,X2)|~entity(X1,X2)),115,['final']). cnf(306,plain,(general(X1,X2)|~abstraction(X1,X2)),85,['final']). cnf(307,plain,(nonhuman(X1,X2)|~abstraction(X1,X2)),88,['final']). cnf(308,plain,(specific(X1,X2)|~eventuality(X1,X2)),145,['final']). cnf(309,plain,(nonexistent(X1,X2)|~eventuality(X1,X2)),142,['final']). cnf(310,plain,(~patient(X1,X2,X3)|~agent(X1,X2,X3)|~nonreflexive(X1,X2)),201,['final']). cnf(311,plain,(~nonexistent(X1,X2)|~existent(X1,X2)),166,['final']). cnf(312,plain,(thing(X1,X2)|~abstraction(X1,X2)),91,['final']). cnf(313,plain,(object(X1,X2)|~substance_matter(X1,X2)),124,['final']). cnf(314,plain,(nonliving(X1,X2)|~object(X1,X2)),109,['final']). cnf(315,plain,(substance_matter(X1,X2)|~food(X1,X2)),127,['final']). cnf(316,plain,(singleton(X1,X2)|~thing(X1,X2)),148,['final']). cnf(317,plain,(~nonliving(X1,X2)|~animate(X1,X2)),163,['final']). cnf(318,plain,(~nonhuman(X1,X2)|~human(X1,X2)),169,['final']). cnf(319,plain,(~specific(X1,X2)|~general(X1,X2)),175,['final']). cnf(320,plain,(~nonliving(X1,X2)|~living(X1,X2)),172,['final']). cnf(321,plain,(X1=X2|~of(X3,X2,X4)|~of(X3,X1,X4)|~forename(X3,X2)|~forename(X3,X1)|~entity(X3,X4)),182,['final']). cnf(322,plain,(~unisex(X1,X2)|~woman(X1,X2)),211,['final']). cnf(323,plain,(relation(X1,X2)|~forename(X1,X2)),209,['final']). cnf(324,plain,(food(X1,X2)|~shake_beverage(X1,X2)),210,['final']). cnf(325,plain,(abstraction(X1,X2)|~forename(X1,X2)),228,['final']). cnf(326,plain,(entity(X1,X2)|~human_person(X1,X2)),212,['final']). cnf(327,plain,(~eventuality(X1,X2)|~existent(X1,X2)),216,['final']). cnf(328,plain,(~eventuality(X1,X2)|~entity(X1,X2)),232,['final']). cnf(329,plain,(substance_matter(X1,X2)|~shake_beverage(X1,X2)),229,['final']). cnf(330,plain,(object(X1,X2)|~shake_beverage(X1,X2)),234,['final']). cnf(331,plain,(~nonliving(X1,X2)|~human_person(X1,X2)),217,['final']). cnf(332,plain,(~object(X1,X2)|~human_person(X1,X2)),237,['final']). cnf(333,plain,(~abstraction(X1,X2)|~human(X1,X2)),218,['final']). cnf(334,plain,(~abstraction(X1,X2)|~human_person(X1,X2)),239,['final']). cnf(335,negated_conjecture,(X1=esk3_0|~of(esk1_0,X1,esk2_0)|~forename(esk1_0,X1)),242,['final']). cnf(336,plain,(~specific(X1,X2)|~abstraction(X1,X2)),219,['final']). cnf(337,plain,(~nonliving(X1,X2)|~organism(X1,X2)),220,['final']). cnf(338,plain,(~eventuality(X1,X2)|~abstraction(X1,X2)),244,['final']). cnf(339,plain,(~object(X1,X2)|~organism(X1,X2)),245,['final']). cnf(340,plain,(~abstraction(X1,X2)|~entity(X1,X2)),243,['final']). cnf(341,plain,(~forename(X1,X2)|~entity(X1,X2)),249,['final']). # SZS output end Saturation.
# Preprocessing time : 0.010 s # Problem is satisfiable (or invalid), generating saturation derivation # SZS status Satisfiable # SZS output start Saturation. fof(1, axiom,a_holds(key(at,t)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_holds_key_at_for_t)). fof(2, axiom,party_of_protocol(a),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_is_party_of_protocol)). fof(3, axiom,message(sent(a,b,pair(a,an_a_nonce))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_sent_message_i_to_b)). fof(4, axiom,a_stored(pair(b,an_a_nonce)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_stored_message_i)). fof(5, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:((message(sent(t,a,triple(encrypt(quadruple(X5,X6,X3,X2),at),X4,X1)))&a_stored(pair(X5,X6)))=>(message(sent(a,X5,pair(X4,encrypt(X1,X3))))&a_holds(key(X3,X5)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', a_forwards_secure)). fof(6, axiom,b_holds(key(bt,t)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', b_hold_key_bt_for_t)). fof(7, axiom,party_of_protocol(b),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', b_is_party_of_protocol)). fof(8, axiom,fresh_to_b(an_a_nonce),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', nonce_a_is_fresh_to_b)). fof(9, axiom,![X1]:![X2]:((message(sent(X1,b,pair(X1,X2)))&fresh_to_b(X2))=>(message(sent(b,t,triple(b,generate_b_nonce(X2),encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))))&b_stored(pair(X1,X2)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', b_creates_freash_nonces_in_time)). fof(10, axiom,![X2]:![X4]:![X5]:(((message(sent(X4,b,pair(encrypt(triple(X4,X2,generate_expiration_time(X5)),bt),encrypt(generate_b_nonce(X5),X2))))&a_key(X2))&b_stored(pair(X4,X5)))=>b_holds(key(X2,X4))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', b_accepts_secure_session_key)). fof(11, axiom,t_holds(key(at,a)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', t_holds_key_at_for_a)). fof(12, axiom,t_holds(key(bt,b)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', t_holds_key_bt_for_b)). fof(13, axiom,party_of_protocol(t),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', t_is_party_of_protocol)). fof(14, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:((((message(sent(X1,t,triple(X1,X2,encrypt(triple(X3,X4,X5),X6))))&t_holds(key(X6,X1)))&t_holds(key(X7,X3)))&a_nonce(X4))=>message(sent(t,X3,triple(encrypt(quadruple(X1,X4,generate_key(X4),X5),X7),encrypt(triple(X3,generate_key(X4),X5),X6),X2)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', server_t_generates_key)). fof(15, axiom,![X1]:![X2]:![X3]:(message(sent(X1,X2,X3))=>intruder_message(X3)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_can_record)). fof(16, axiom,![X1]:![X2]:(intruder_message(pair(X1,X2))=>(intruder_message(X1)&intruder_message(X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_decomposes_pairs)). fof(17, axiom,![X1]:![X2]:![X3]:(intruder_message(triple(X1,X2,X3))=>((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_decomposes_triples)). fof(18, axiom,![X1]:![X2]:![X3]:![X4]:(intruder_message(quadruple(X1,X2,X3,X4))=>(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))&intruder_message(X4))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_decomposes_quadruples)). fof(19, axiom,![X1]:![X2]:((intruder_message(X1)&intruder_message(X2))=>intruder_message(pair(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_composes_pairs)). fof(20, axiom,![X1]:![X2]:![X3]:(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))=>intruder_message(triple(X1,X2,X3))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_composes_triples)). fof(21, axiom,![X1]:![X2]:![X3]:![X4]:((((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))&intruder_message(X4))=>intruder_message(quadruple(X1,X2,X3,X4))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_composes_quadruples)). fof(22, axiom,![X1]:![X2]:![X3]:(((intruder_message(encrypt(X1,X2))&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(X2)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_interception)). fof(23, axiom,![X1]:![X2]:![X3]:(((intruder_message(X1)&party_of_protocol(X2))&party_of_protocol(X3))=>message(sent(X2,X3,X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_message_sent)). fof(24, axiom,![X2]:![X3]:((intruder_message(X2)&party_of_protocol(X3))=>intruder_holds(key(X2,X3))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_holds_key)). fof(25, axiom,![X1]:![X2]:![X3]:(((intruder_message(X1)&intruder_holds(key(X2,X3)))&party_of_protocol(X3))=>intruder_message(encrypt(X1,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', intruder_key_encrypts)). fof(26, axiom,a_nonce(an_a_nonce),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', an_a_nonce_is_a_nonce)). fof(27, axiom,![X1]:~(a_nonce(generate_key(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', generated_keys_are_not_nonces)). fof(28, axiom,![X1]:(a_nonce(generate_expiration_time(X1))&a_nonce(generate_b_nonce(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', generated_times_and_nonces_are_nonces)). fof(29, axiom,![X1]:~((a_key(X1)&a_nonce(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', nothing_is_a_nonce_and_a_key)). fof(30, axiom,![X1]:a_key(generate_key(X1)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', generated_keys_are_keys)). fof(31, axiom,fresh_intruder_nonce(an_intruder_nonce),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', an_intruder_nonce_is_a_fresh_intruder_nonce)). fof(32, axiom,![X1]:(fresh_intruder_nonce(X1)=>fresh_intruder_nonce(generate_intruder_nonce(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', can_generate_more_fresh_intruder_nonces)). fof(33, axiom,![X1]:(fresh_intruder_nonce(X1)=>(fresh_to_b(X1)&intruder_message(X1))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SWV017+1.p', fresh_intruder_nonces_are_fresh_to_b)). fof(34, plain,![X1]:~(a_nonce(generate_key(X1))),inference(fof_simplification,[status(thm)],[27,theory(equality)])). cnf(35,plain,(a_holds(key(at,t))),inference(split_conjunct,[status(thm)],[1])). cnf(36,plain,(party_of_protocol(a)),inference(split_conjunct,[status(thm)],[2])). cnf(37,plain,(message(sent(a,b,pair(a,an_a_nonce)))),inference(split_conjunct,[status(thm)],[3])). cnf(38,plain,(a_stored(pair(b,an_a_nonce))),inference(split_conjunct,[status(thm)],[4])). fof(39, plain,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:((~(message(sent(t,a,triple(encrypt(quadruple(X5,X6,X3,X2),at),X4,X1))))|~(a_stored(pair(X5,X6))))|(message(sent(a,X5,pair(X4,encrypt(X1,X3))))&a_holds(key(X3,X5)))),inference(fof_nnf,[status(thm)],[5])). fof(40, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:((~(message(sent(t,a,triple(encrypt(quadruple(X11,X12,X9,X8),at),X10,X7))))|~(a_stored(pair(X11,X12))))|(message(sent(a,X11,pair(X10,encrypt(X7,X9))))&a_holds(key(X9,X11)))),inference(variable_rename,[status(thm)],[39])). fof(41, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X12]:((message(sent(a,X11,pair(X10,encrypt(X7,X9))))|(~(message(sent(t,a,triple(encrypt(quadruple(X11,X12,X9,X8),at),X10,X7))))|~(a_stored(pair(X11,X12)))))&(a_holds(key(X9,X11))|(~(message(sent(t,a,triple(encrypt(quadruple(X11,X12,X9,X8),at),X10,X7))))|~(a_stored(pair(X11,X12)))))),inference(distribute,[status(thm)],[40])). cnf(42,plain,(a_holds(key(X3,X1))|~a_stored(pair(X1,X2))|~message(sent(t,a,triple(encrypt(quadruple(X1,X2,X3,X4),at),X5,X6)))),inference(split_conjunct,[status(thm)],[41])). cnf(43,plain,(message(sent(a,X1,pair(X5,encrypt(X6,X3))))|~a_stored(pair(X1,X2))|~message(sent(t,a,triple(encrypt(quadruple(X1,X2,X3,X4),at),X5,X6)))),inference(split_conjunct,[status(thm)],[41])). cnf(44,plain,(b_holds(key(bt,t))),inference(split_conjunct,[status(thm)],[6])). cnf(45,plain,(party_of_protocol(b)),inference(split_conjunct,[status(thm)],[7])). cnf(46,plain,(fresh_to_b(an_a_nonce)),inference(split_conjunct,[status(thm)],[8])). fof(47, plain,![X1]:![X2]:((~(message(sent(X1,b,pair(X1,X2))))|~(fresh_to_b(X2)))|(message(sent(b,t,triple(b,generate_b_nonce(X2),encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))))&b_stored(pair(X1,X2)))),inference(fof_nnf,[status(thm)],[9])). fof(48, plain,![X3]:![X4]:((~(message(sent(X3,b,pair(X3,X4))))|~(fresh_to_b(X4)))|(message(sent(b,t,triple(b,generate_b_nonce(X4),encrypt(triple(X3,X4,generate_expiration_time(X4)),bt))))&b_stored(pair(X3,X4)))),inference(variable_rename,[status(thm)],[47])). fof(49, plain,![X3]:![X4]:((message(sent(b,t,triple(b,generate_b_nonce(X4),encrypt(triple(X3,X4,generate_expiration_time(X4)),bt))))|(~(message(sent(X3,b,pair(X3,X4))))|~(fresh_to_b(X4))))&(b_stored(pair(X3,X4))|(~(message(sent(X3,b,pair(X3,X4))))|~(fresh_to_b(X4))))),inference(distribute,[status(thm)],[48])). cnf(50,plain,(b_stored(pair(X2,X1))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))),inference(split_conjunct,[status(thm)],[49])). cnf(51,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))),inference(split_conjunct,[status(thm)],[49])). fof(52, plain,![X2]:![X4]:![X5]:(((~(message(sent(X4,b,pair(encrypt(triple(X4,X2,generate_expiration_time(X5)),bt),encrypt(generate_b_nonce(X5),X2)))))|~(a_key(X2)))|~(b_stored(pair(X4,X5))))|b_holds(key(X2,X4))),inference(fof_nnf,[status(thm)],[10])). fof(53, plain,![X6]:![X7]:![X8]:(((~(message(sent(X7,b,pair(encrypt(triple(X7,X6,generate_expiration_time(X8)),bt),encrypt(generate_b_nonce(X8),X6)))))|~(a_key(X6)))|~(b_stored(pair(X7,X8))))|b_holds(key(X6,X7))),inference(variable_rename,[status(thm)],[52])). cnf(54,plain,(b_holds(key(X1,X2))|~b_stored(pair(X2,X3))|~a_key(X1)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))),inference(split_conjunct,[status(thm)],[53])). cnf(55,plain,(t_holds(key(at,a))),inference(split_conjunct,[status(thm)],[11])). cnf(56,plain,(t_holds(key(bt,b))),inference(split_conjunct,[status(thm)],[12])). cnf(57,plain,(party_of_protocol(t)),inference(split_conjunct,[status(thm)],[13])). fof(58, plain,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:((((~(message(sent(X1,t,triple(X1,X2,encrypt(triple(X3,X4,X5),X6)))))|~(t_holds(key(X6,X1))))|~(t_holds(key(X7,X3))))|~(a_nonce(X4)))|message(sent(t,X3,triple(encrypt(quadruple(X1,X4,generate_key(X4),X5),X7),encrypt(triple(X3,generate_key(X4),X5),X6),X2)))),inference(fof_nnf,[status(thm)],[14])). fof(59, plain,![X8]:![X9]:![X10]:![X11]:![X12]:![X13]:![X14]:((((~(message(sent(X8,t,triple(X8,X9,encrypt(triple(X10,X11,X12),X13)))))|~(t_holds(key(X13,X8))))|~(t_holds(key(X14,X10))))|~(a_nonce(X11)))|message(sent(t,X10,triple(encrypt(quadruple(X8,X11,generate_key(X11),X12),X14),encrypt(triple(X10,generate_key(X11),X12),X13),X9)))),inference(variable_rename,[status(thm)],[58])). cnf(60,plain,(message(sent(t,X1,triple(encrypt(quadruple(X2,X3,generate_key(X3),X4),X5),encrypt(triple(X1,generate_key(X3),X4),X6),X7)))|~a_nonce(X3)|~t_holds(key(X5,X1))|~t_holds(key(X6,X2))|~message(sent(X2,t,triple(X2,X7,encrypt(triple(X1,X3,X4),X6))))),inference(split_conjunct,[status(thm)],[59])). fof(61, plain,![X1]:![X2]:![X3]:(~(message(sent(X1,X2,X3)))|intruder_message(X3)),inference(fof_nnf,[status(thm)],[15])). fof(62, plain,![X4]:![X5]:![X6]:(~(message(sent(X4,X5,X6)))|intruder_message(X6)),inference(variable_rename,[status(thm)],[61])). cnf(63,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))),inference(split_conjunct,[status(thm)],[62])). fof(64, plain,![X1]:![X2]:(~(intruder_message(pair(X1,X2)))|(intruder_message(X1)&intruder_message(X2))),inference(fof_nnf,[status(thm)],[16])). fof(65, plain,![X3]:![X4]:(~(intruder_message(pair(X3,X4)))|(intruder_message(X3)&intruder_message(X4))),inference(variable_rename,[status(thm)],[64])). fof(66, plain,![X3]:![X4]:((intruder_message(X3)|~(intruder_message(pair(X3,X4))))&(intruder_message(X4)|~(intruder_message(pair(X3,X4))))),inference(distribute,[status(thm)],[65])). cnf(67,plain,(intruder_message(X2)|~intruder_message(pair(X1,X2))),inference(split_conjunct,[status(thm)],[66])). cnf(68,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))),inference(split_conjunct,[status(thm)],[66])). fof(69, plain,![X1]:![X2]:![X3]:(~(intruder_message(triple(X1,X2,X3)))|((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))),inference(fof_nnf,[status(thm)],[17])). fof(70, plain,![X4]:![X5]:![X6]:(~(intruder_message(triple(X4,X5,X6)))|((intruder_message(X4)&intruder_message(X5))&intruder_message(X6))),inference(variable_rename,[status(thm)],[69])). fof(71, plain,![X4]:![X5]:![X6]:(((intruder_message(X4)|~(intruder_message(triple(X4,X5,X6))))&(intruder_message(X5)|~(intruder_message(triple(X4,X5,X6)))))&(intruder_message(X6)|~(intruder_message(triple(X4,X5,X6))))),inference(distribute,[status(thm)],[70])). cnf(72,plain,(intruder_message(X3)|~intruder_message(triple(X1,X2,X3))),inference(split_conjunct,[status(thm)],[71])). cnf(73,plain,(intruder_message(X2)|~intruder_message(triple(X1,X2,X3))),inference(split_conjunct,[status(thm)],[71])). cnf(74,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))),inference(split_conjunct,[status(thm)],[71])). fof(75, plain,![X1]:![X2]:![X3]:![X4]:(~(intruder_message(quadruple(X1,X2,X3,X4)))|(((intruder_message(X1)&intruder_message(X2))&intruder_message(X3))&intruder_message(X4))),inference(fof_nnf,[status(thm)],[18])). fof(76, plain,![X5]:![X6]:![X7]:![X8]:(~(intruder_message(quadruple(X5,X6,X7,X8)))|(((intruder_message(X5)&intruder_message(X6))&intruder_message(X7))&intruder_message(X8))),inference(variable_rename,[status(thm)],[75])). fof(77, plain,![X5]:![X6]:![X7]:![X8]:((((intruder_message(X5)|~(intruder_message(quadruple(X5,X6,X7,X8))))&(intruder_message(X6)|~(intruder_message(quadruple(X5,X6,X7,X8)))))&(intruder_message(X7)|~(intruder_message(quadruple(X5,X6,X7,X8)))))&(intruder_message(X8)|~(intruder_message(quadruple(X5,X6,X7,X8))))),inference(distribute,[status(thm)],[76])). cnf(78,plain,(intruder_message(X4)|~intruder_message(quadruple(X1,X2,X3,X4))),inference(split_conjunct,[status(thm)],[77])). cnf(79,plain,(intruder_message(X3)|~intruder_message(quadruple(X1,X2,X3,X4))),inference(split_conjunct,[status(thm)],[77])). cnf(80,plain,(intruder_message(X2)|~intruder_message(quadruple(X1,X2,X3,X4))),inference(split_conjunct,[status(thm)],[77])). cnf(81,plain,(intruder_message(X1)|~intruder_message(quadruple(X1,X2,X3,X4))),inference(split_conjunct,[status(thm)],[77])). fof(82, plain,![X1]:![X2]:((~(intruder_message(X1))|~(intruder_message(X2)))|intruder_message(pair(X1,X2))),inference(fof_nnf,[status(thm)],[19])). fof(83, plain,![X3]:![X4]:((~(intruder_message(X3))|~(intruder_message(X4)))|intruder_message(pair(X3,X4))),inference(variable_rename,[status(thm)],[82])). cnf(84,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[83])). fof(85, plain,![X1]:![X2]:![X3]:(((~(intruder_message(X1))|~(intruder_message(X2)))|~(intruder_message(X3)))|intruder_message(triple(X1,X2,X3))),inference(fof_nnf,[status(thm)],[20])). fof(86, plain,![X4]:![X5]:![X6]:(((~(intruder_message(X4))|~(intruder_message(X5)))|~(intruder_message(X6)))|intruder_message(triple(X4,X5,X6))),inference(variable_rename,[status(thm)],[85])). cnf(87,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[86])). fof(88, plain,![X1]:![X2]:![X3]:![X4]:((((~(intruder_message(X1))|~(intruder_message(X2)))|~(intruder_message(X3)))|~(intruder_message(X4)))|intruder_message(quadruple(X1,X2,X3,X4))),inference(fof_nnf,[status(thm)],[21])). fof(89, plain,![X5]:![X6]:![X7]:![X8]:((((~(intruder_message(X5))|~(intruder_message(X6)))|~(intruder_message(X7)))|~(intruder_message(X8)))|intruder_message(quadruple(X5,X6,X7,X8))),inference(variable_rename,[status(thm)],[88])). cnf(90,plain,(intruder_message(quadruple(X1,X2,X3,X4))|~intruder_message(X4)|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[89])). fof(91, plain,![X1]:![X2]:![X3]:(((~(intruder_message(encrypt(X1,X2)))|~(intruder_holds(key(X2,X3))))|~(party_of_protocol(X3)))|intruder_message(X2)),inference(fof_nnf,[status(thm)],[22])). fof(92, plain,![X4]:![X5]:![X6]:(((~(intruder_message(encrypt(X4,X5)))|~(intruder_holds(key(X5,X6))))|~(party_of_protocol(X6)))|intruder_message(X5)),inference(variable_rename,[status(thm)],[91])). cnf(93,plain,(intruder_message(X1)|~party_of_protocol(X2)|~intruder_holds(key(X1,X2))|~intruder_message(encrypt(X3,X1))),inference(split_conjunct,[status(thm)],[92])). fof(94, plain,![X1]:![X2]:![X3]:(((~(intruder_message(X1))|~(party_of_protocol(X2)))|~(party_of_protocol(X3)))|message(sent(X2,X3,X1))),inference(fof_nnf,[status(thm)],[23])). fof(95, plain,![X4]:![X5]:![X6]:(((~(intruder_message(X4))|~(party_of_protocol(X5)))|~(party_of_protocol(X6)))|message(sent(X5,X6,X4))),inference(variable_rename,[status(thm)],[94])). cnf(96,plain,(message(sent(X1,X2,X3))|~party_of_protocol(X2)|~party_of_protocol(X1)|~intruder_message(X3)),inference(split_conjunct,[status(thm)],[95])). fof(97, plain,![X2]:![X3]:((~(intruder_message(X2))|~(party_of_protocol(X3)))|intruder_holds(key(X2,X3))),inference(fof_nnf,[status(thm)],[24])). fof(98, plain,![X4]:![X5]:((~(intruder_message(X4))|~(party_of_protocol(X5)))|intruder_holds(key(X4,X5))),inference(variable_rename,[status(thm)],[97])). cnf(99,plain,(intruder_holds(key(X1,X2))|~party_of_protocol(X2)|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[98])). fof(100, plain,![X1]:![X2]:![X3]:(((~(intruder_message(X1))|~(intruder_holds(key(X2,X3))))|~(party_of_protocol(X3)))|intruder_message(encrypt(X1,X2))),inference(fof_nnf,[status(thm)],[25])). fof(101, plain,![X4]:![X5]:![X6]:(((~(intruder_message(X4))|~(intruder_holds(key(X5,X6))))|~(party_of_protocol(X6)))|intruder_message(encrypt(X4,X5))),inference(variable_rename,[status(thm)],[100])). cnf(102,plain,(intruder_message(encrypt(X1,X2))|~party_of_protocol(X3)|~intruder_holds(key(X2,X3))|~intruder_message(X1)),inference(split_conjunct,[status(thm)],[101])). cnf(103,plain,(a_nonce(an_a_nonce)),inference(split_conjunct,[status(thm)],[26])). fof(104, plain,![X2]:~(a_nonce(generate_key(X2))),inference(variable_rename,[status(thm)],[34])). cnf(105,plain,(~a_nonce(generate_key(X1))),inference(split_conjunct,[status(thm)],[104])). fof(106, plain,![X2]:(a_nonce(generate_expiration_time(X2))&a_nonce(generate_b_nonce(X2))),inference(variable_rename,[status(thm)],[28])). cnf(107,plain,(a_nonce(generate_b_nonce(X1))),inference(split_conjunct,[status(thm)],[106])). cnf(108,plain,(a_nonce(generate_expiration_time(X1))),inference(split_conjunct,[status(thm)],[106])). fof(109, plain,![X1]:(~(a_key(X1))|~(a_nonce(X1))),inference(fof_nnf,[status(thm)],[29])). fof(110, plain,![X2]:(~(a_key(X2))|~(a_nonce(X2))),inference(variable_rename,[status(thm)],[109])). cnf(111,plain,(~a_nonce(X1)|~a_key(X1)),inference(split_conjunct,[status(thm)],[110])). fof(112, plain,![X2]:a_key(generate_key(X2)),inference(variable_rename,[status(thm)],[30])). cnf(113,plain,(a_key(generate_key(X1))),inference(split_conjunct,[status(thm)],[112])). cnf(114,plain,(fresh_intruder_nonce(an_intruder_nonce)),inference(split_conjunct,[status(thm)],[31])). fof(115, plain,![X1]:(~(fresh_intruder_nonce(X1))|fresh_intruder_nonce(generate_intruder_nonce(X1))),inference(fof_nnf,[status(thm)],[32])). fof(116, plain,![X2]:(~(fresh_intruder_nonce(X2))|fresh_intruder_nonce(generate_intruder_nonce(X2))),inference(variable_rename,[status(thm)],[115])). cnf(117,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),inference(split_conjunct,[status(thm)],[116])). fof(118, plain,![X1]:(~(fresh_intruder_nonce(X1))|(fresh_to_b(X1)&intruder_message(X1))),inference(fof_nnf,[status(thm)],[33])). fof(119, plain,![X2]:(~(fresh_intruder_nonce(X2))|(fresh_to_b(X2)&intruder_message(X2))),inference(variable_rename,[status(thm)],[118])). fof(120, plain,![X2]:((fresh_to_b(X2)|~(fresh_intruder_nonce(X2)))&(intruder_message(X2)|~(fresh_intruder_nonce(X2)))),inference(distribute,[status(thm)],[119])). cnf(121,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)),inference(split_conjunct,[status(thm)],[120])). cnf(122,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)),inference(split_conjunct,[status(thm)],[120])). cnf(123,plain,(intruder_message(an_intruder_nonce)),inference(spm,[status(thm)],[121,114,theory(equality)])). cnf(125,plain,(intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),inference(spm,[status(thm)],[121,117,theory(equality)])). cnf(126,plain,(intruder_message(pair(a,an_a_nonce))),inference(spm,[status(thm)],[63,37,theory(equality)])). cnf(133,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~party_of_protocol(X3)|~intruder_message(X2)),inference(spm,[status(thm)],[102,99,theory(equality)])). cnf(135,plain,(b_stored(pair(a,an_a_nonce))|~fresh_to_b(an_a_nonce)),inference(spm,[status(thm)],[50,37,theory(equality)])). cnf(136,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~intruder_message(pair(X1,X2))|~party_of_protocol(b)|~party_of_protocol(X1)),inference(spm,[status(thm)],[50,96,theory(equality)])). cnf(137,plain,(b_stored(pair(a,an_a_nonce))|$false),inference(rw,[status(thm)],[135,46,theory(equality)])). cnf(138,plain,(b_stored(pair(a,an_a_nonce))),inference(cn,[status(thm)],[137,theory(equality)])). cnf(139,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~intruder_message(pair(X1,X2))|$false|~party_of_protocol(X1)),inference(rw,[status(thm)],[136,45,theory(equality)])). cnf(140,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~intruder_message(pair(X1,X2))|~party_of_protocol(X1)),inference(cn,[status(thm)],[139,theory(equality)])). cnf(145,plain,(a_holds(key(X1,b))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4)))),inference(spm,[status(thm)],[42,38,theory(equality)])). cnf(146,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2)))),inference(spm,[status(thm)],[43,38,theory(equality)])). cnf(147,plain,(message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))|~fresh_to_b(an_a_nonce)),inference(spm,[status(thm)],[51,37,theory(equality)])). cnf(148,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~intruder_message(pair(X2,X1))|~party_of_protocol(b)|~party_of_protocol(X2)),inference(spm,[status(thm)],[51,96,theory(equality)])). cnf(149,plain,(message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))|$false),inference(rw,[status(thm)],[147,46,theory(equality)])). cnf(150,plain,(message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))),inference(cn,[status(thm)],[149,theory(equality)])). cnf(151,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~intruder_message(pair(X2,X1))|$false|~party_of_protocol(X2)),inference(rw,[status(thm)],[148,45,theory(equality)])). cnf(152,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~intruder_message(pair(X2,X1))|~party_of_protocol(X2)),inference(cn,[status(thm)],[151,theory(equality)])). cnf(153,plain,(message(sent(t,X1,triple(encrypt(quadruple(b,X2,generate_key(X2),X3),X4),encrypt(triple(X1,generate_key(X2),X3),bt),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(b,t,triple(b,X5,encrypt(triple(X1,X2,X3),bt))))),inference(spm,[status(thm)],[60,56,theory(equality)])). cnf(154,plain,(message(sent(t,X1,triple(encrypt(quadruple(a,X2,generate_key(X2),X3),X4),encrypt(triple(X1,generate_key(X2),X3),at),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(a,t,triple(a,X5,encrypt(triple(X1,X2,X3),at))))),inference(spm,[status(thm)],[60,55,theory(equality)])). cnf(155,plain,(intruder_message(a)),inference(spm,[status(thm)],[68,126,theory(equality)])). cnf(156,plain,(intruder_message(an_a_nonce)),inference(spm,[status(thm)],[67,126,theory(equality)])). cnf(157,plain,(b_holds(key(X1,a))|~a_key(X1)|~message(sent(a,b,pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1))))),inference(spm,[status(thm)],[54,138,theory(equality)])). cnf(158,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[133,45,theory(equality)])). cnf(162,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[140,84,theory(equality)])). cnf(167,plain,(b_holds(key(X1,X2))|~a_key(X1)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))|~intruder_message(X3)|~intruder_message(X2)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(spm,[status(thm)],[54,162,theory(equality)])). cnf(168,plain,(intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))),inference(spm,[status(thm)],[63,150,theory(equality)])). cnf(169,plain,(a_holds(key(X1,b))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4))|~party_of_protocol(a)|~party_of_protocol(t)),inference(spm,[status(thm)],[145,96,theory(equality)])). cnf(170,plain,(a_holds(key(X1,b))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4))|$false|~party_of_protocol(t)),inference(rw,[status(thm)],[169,36,theory(equality)])). cnf(171,plain,(a_holds(key(X1,b))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4))|$false|$false),inference(rw,[status(thm)],[170,57,theory(equality)])). cnf(172,plain,(a_holds(key(X1,b))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4))),inference(cn,[status(thm)],[171,theory(equality)])). cnf(173,plain,(a_holds(key(X1,b))|~intruder_message(X4)|~intruder_message(X3)|~intruder_message(encrypt(quadruple(b,an_a_nonce,X1,X2),at))),inference(spm,[status(thm)],[172,87,theory(equality)])). cnf(174,plain,(a_holds(key(X1,b))|~intruder_message(X3)|~intruder_message(X4)|~intruder_message(quadruple(b,an_a_nonce,X1,X2))|~intruder_message(at)),inference(spm,[status(thm)],[173,158,theory(equality)])). cnf(175,plain,(intruder_message(b)),inference(spm,[status(thm)],[74,168,theory(equality)])). cnf(176,plain,(intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[72,168,theory(equality)])). cnf(177,plain,(intruder_message(generate_b_nonce(an_a_nonce))),inference(spm,[status(thm)],[73,168,theory(equality)])). cnf(178,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|~party_of_protocol(b)|~party_of_protocol(a)),inference(spm,[status(thm)],[157,96,theory(equality)])). cnf(179,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|$false|~party_of_protocol(a)),inference(rw,[status(thm)],[178,45,theory(equality)])). cnf(180,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|$false|$false),inference(rw,[status(thm)],[179,36,theory(equality)])). cnf(181,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))),inference(cn,[status(thm)],[180,theory(equality)])). cnf(182,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2))|~party_of_protocol(a)|~party_of_protocol(t)),inference(spm,[status(thm)],[146,96,theory(equality)])). cnf(183,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2))|$false|~party_of_protocol(t)),inference(rw,[status(thm)],[182,36,theory(equality)])). cnf(184,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2))|$false|$false),inference(rw,[status(thm)],[183,57,theory(equality)])). cnf(185,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2))),inference(cn,[status(thm)],[184,theory(equality)])). cnf(187,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~party_of_protocol(X2)|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[152,84,theory(equality)])). cnf(192,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(X2)|~intruder_message(X1)|~intruder_message(encrypt(quadruple(b,an_a_nonce,X3,X4),at))),inference(spm,[status(thm)],[185,87,theory(equality)])). cnf(193,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(X2)|~intruder_message(X1)|~intruder_message(quadruple(b,an_a_nonce,X3,X4))|~intruder_message(at)),inference(spm,[status(thm)],[192,158,theory(equality)])). cnf(194,plain,(b_holds(key(X1,a))|~a_key(X1)|~intruder_message(encrypt(generate_b_nonce(an_a_nonce),X1))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[181,84,theory(equality)])). cnf(195,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~a_key(X1)|~intruder_message(generate_b_nonce(an_a_nonce))|~intruder_message(X1)),inference(spm,[status(thm)],[194,158,theory(equality)])). cnf(196,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~a_key(X1)|$false|~intruder_message(X1)),inference(rw,[status(thm)],[195,177,theory(equality)])). cnf(197,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~a_key(X1)|~intruder_message(X1)),inference(cn,[status(thm)],[196,theory(equality)])). cnf(198,plain,(b_holds(key(X1,a))|~intruder_message(X1)|~a_key(X1)|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)),inference(spm,[status(thm)],[197,158,theory(equality)])). cnf(199,plain,(b_holds(key(an_a_nonce,a))|~intruder_message(an_a_nonce)|~a_key(an_a_nonce)),inference(spm,[status(thm)],[197,176,theory(equality)])). cnf(200,plain,(b_holds(key(an_a_nonce,a))|$false|~a_key(an_a_nonce)),inference(rw,[status(thm)],[199,156,theory(equality)])). cnf(201,plain,(b_holds(key(an_a_nonce,a))|~a_key(an_a_nonce)),inference(cn,[status(thm)],[200,theory(equality)])). cnf(202,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(b,X1,X2),bt))))),inference(spm,[status(thm)],[153,56,theory(equality)])). cnf(203,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(a,X1,X2),bt))))),inference(spm,[status(thm)],[153,55,theory(equality)])). cnf(204,plain,(b_holds(key(X1,a))|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)),inference(csr,[status(thm)],[198,73])). cnf(205,plain,(intruder_message(triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt)))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)),inference(spm,[status(thm)],[63,187,theory(equality)])). cnf(207,plain,(intruder_message(encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)),inference(spm,[status(thm)],[72,205,theory(equality)])). cnf(208,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)),inference(spm,[status(thm)],[73,205,theory(equality)])). cnf(216,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(triple(b,X3,encrypt(triple(b,X1,X2),bt)))|~party_of_protocol(t)|~party_of_protocol(b)),inference(spm,[status(thm)],[202,96,theory(equality)])). cnf(217,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~a_nonce(X1)|~intruder_message(X1)|~intruder_message(b)|~fresh_to_b(X1)|~party_of_protocol(b)),inference(spm,[status(thm)],[202,187,theory(equality)])). cnf(218,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(triple(b,X3,encrypt(triple(b,X1,X2),bt)))|$false|~party_of_protocol(b)),inference(rw,[status(thm)],[216,57,theory(equality)])). cnf(219,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(triple(b,X3,encrypt(triple(b,X1,X2),bt)))|$false|$false),inference(rw,[status(thm)],[218,45,theory(equality)])). cnf(220,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(triple(b,X3,encrypt(triple(b,X1,X2),bt)))),inference(cn,[status(thm)],[219,theory(equality)])). cnf(221,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~a_nonce(X1)|~intruder_message(X1)|$false|~fresh_to_b(X1)|~party_of_protocol(b)),inference(rw,[status(thm)],[217,175,theory(equality)])). cnf(222,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~a_nonce(X1)|~intruder_message(X1)|$false|~fresh_to_b(X1)|$false),inference(rw,[status(thm)],[221,45,theory(equality)])). cnf(223,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~a_nonce(X1)|~intruder_message(X1)|~fresh_to_b(X1)),inference(cn,[status(thm)],[222,theory(equality)])). cnf(224,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|~party_of_protocol(b)),inference(spm,[status(thm)],[167,96,theory(equality)])). cnf(225,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|$false),inference(rw,[status(thm)],[224,45,theory(equality)])). cnf(226,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))),inference(cn,[status(thm)],[225,theory(equality)])). cnf(227,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(b,X1,X2),at))))),inference(spm,[status(thm)],[154,56,theory(equality)])). cnf(228,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(a,X1,X2),at))))),inference(spm,[status(thm)],[154,55,theory(equality)])). cnf(229,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(encrypt(generate_b_nonce(X3),X1))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))),inference(spm,[status(thm)],[226,84,theory(equality)])). cnf(230,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(generate_b_nonce(X3))|~intruder_message(X1)),inference(spm,[status(thm)],[229,158,theory(equality)])). cnf(231,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X1)|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(csr,[status(thm)],[230,208])). cnf(232,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)),inference(spm,[status(thm)],[231,158,theory(equality)])). cnf(234,plain,(b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)),inference(spm,[status(thm)],[231,207,theory(equality)])). cnf(240,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(csr,[status(thm)],[232,73])). cnf(241,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),inference(csr,[status(thm)],[240,74])). cnf(242,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(b,X1,X2),bt))|~intruder_message(X3)|~intruder_message(b)),inference(spm,[status(thm)],[220,87,theory(equality)])). cnf(244,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(b,X1,X2),bt))|~intruder_message(X3)|$false),inference(rw,[status(thm)],[242,175,theory(equality)])). cnf(245,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(b,X1,X2),bt))|~intruder_message(X3)),inference(cn,[status(thm)],[244,theory(equality)])). cnf(249,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[63,223,theory(equality)])). cnf(250,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(triple(b,X3,encrypt(triple(a,X1,X2),bt)))|~party_of_protocol(t)|~party_of_protocol(b)),inference(spm,[status(thm)],[203,96,theory(equality)])). cnf(251,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~a_nonce(X1)|~intruder_message(X1)|~intruder_message(a)|~fresh_to_b(X1)|~party_of_protocol(a)),inference(spm,[status(thm)],[203,187,theory(equality)])). cnf(252,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce))))|~a_nonce(an_a_nonce)),inference(spm,[status(thm)],[203,150,theory(equality)])). cnf(253,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(triple(b,X3,encrypt(triple(a,X1,X2),bt)))|$false|~party_of_protocol(b)),inference(rw,[status(thm)],[250,57,theory(equality)])). cnf(254,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(triple(b,X3,encrypt(triple(a,X1,X2),bt)))|$false|$false),inference(rw,[status(thm)],[253,45,theory(equality)])). cnf(255,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(triple(b,X3,encrypt(triple(a,X1,X2),bt)))),inference(cn,[status(thm)],[254,theory(equality)])). cnf(256,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~a_nonce(X1)|~intruder_message(X1)|$false|~fresh_to_b(X1)|~party_of_protocol(a)),inference(rw,[status(thm)],[251,155,theory(equality)])). cnf(257,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~a_nonce(X1)|~intruder_message(X1)|$false|~fresh_to_b(X1)|$false),inference(rw,[status(thm)],[256,36,theory(equality)])). cnf(258,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~a_nonce(X1)|~intruder_message(X1)|~fresh_to_b(X1)),inference(cn,[status(thm)],[257,theory(equality)])). cnf(259,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce))))|$false),inference(rw,[status(thm)],[252,103,theory(equality)])). cnf(260,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce))))),inference(cn,[status(thm)],[259,theory(equality)])). cnf(261,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(X3)|~a_nonce(X1)|~intruder_message(triple(b,X1,X2))|~intruder_message(bt)),inference(spm,[status(thm)],[245,158,theory(equality)])). cnf(262,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~a_nonce(X1)|~intruder_message(X1)|~intruder_message(b)|~fresh_to_b(X1)|~party_of_protocol(b)),inference(spm,[status(thm)],[245,207,theory(equality)])). cnf(263,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~a_nonce(X1)|~intruder_message(X1)|$false|~fresh_to_b(X1)|~party_of_protocol(b)),inference(rw,[status(thm)],[262,175,theory(equality)])). cnf(264,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~a_nonce(X1)|~intruder_message(X1)|$false|~fresh_to_b(X1)|$false),inference(rw,[status(thm)],[263,45,theory(equality)])). cnf(265,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~a_nonce(X1)|~intruder_message(X1)|~fresh_to_b(X1)),inference(cn,[status(thm)],[264,theory(equality)])). cnf(266,plain,(intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[74,249,theory(equality)])). cnf(267,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[72,249,theory(equality)])). cnf(268,plain,(intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[73,249,theory(equality)])). cnf(269,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|~intruder_message(b)|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(b)|~a_nonce(X1)),inference(spm,[status(thm)],[231,268,theory(equality)])). cnf(271,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|$false|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(b)|~a_nonce(X1)),inference(rw,[status(thm)],[269,175,theory(equality)])). cnf(272,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|$false|~intruder_message(generate_key(X1))|$false|~fresh_to_b(X1)|~party_of_protocol(b)|~a_nonce(X1)),inference(rw,[status(thm)],[271,113,theory(equality)])). cnf(273,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|$false|~intruder_message(generate_key(X1))|$false|~fresh_to_b(X1)|$false|~a_nonce(X1)),inference(rw,[status(thm)],[272,45,theory(equality)])). cnf(274,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(X1)|~intruder_message(generate_key(X1))|~fresh_to_b(X1)|~a_nonce(X1)),inference(cn,[status(thm)],[273,theory(equality)])). cnf(275,plain,(intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce)))),inference(spm,[status(thm)],[63,260,theory(equality)])). cnf(276,plain,(a_holds(key(generate_key(an_a_nonce),b))),inference(spm,[status(thm)],[145,260,theory(equality)])). cnf(277,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))))),inference(spm,[status(thm)],[146,260,theory(equality)])). cnf(278,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(triple(a,X3,encrypt(triple(b,X1,X2),at)))|~party_of_protocol(t)|~party_of_protocol(a)),inference(spm,[status(thm)],[227,96,theory(equality)])). cnf(279,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(triple(a,X3,encrypt(triple(b,X1,X2),at)))|$false|~party_of_protocol(a)),inference(rw,[status(thm)],[278,57,theory(equality)])). cnf(280,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(triple(a,X3,encrypt(triple(b,X1,X2),at)))|$false|$false),inference(rw,[status(thm)],[279,36,theory(equality)])). cnf(281,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(triple(a,X3,encrypt(triple(b,X1,X2),at)))),inference(cn,[status(thm)],[280,theory(equality)])). cnf(282,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))),inference(spm,[status(thm)],[63,277,theory(equality)])). cnf(283,plain,(b_holds(key(generate_key(an_a_nonce),a))|~intruder_message(an_a_nonce)|~intruder_message(a)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(spm,[status(thm)],[167,277,theory(equality)])). cnf(285,plain,(b_holds(key(generate_key(an_a_nonce),a))|$false|~intruder_message(a)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(rw,[status(thm)],[283,156,theory(equality)])). cnf(286,plain,(b_holds(key(generate_key(an_a_nonce),a))|$false|$false|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(rw,[status(thm)],[285,155,theory(equality)])). cnf(287,plain,(b_holds(key(generate_key(an_a_nonce),a))|$false|$false|$false|~fresh_to_b(an_a_nonce)|~party_of_protocol(a)),inference(rw,[status(thm)],[286,113,theory(equality)])). cnf(288,plain,(b_holds(key(generate_key(an_a_nonce),a))|$false|$false|$false|$false|~party_of_protocol(a)),inference(rw,[status(thm)],[287,46,theory(equality)])). cnf(289,plain,(b_holds(key(generate_key(an_a_nonce),a))|$false|$false|$false|$false|$false),inference(rw,[status(thm)],[288,36,theory(equality)])). cnf(290,plain,(b_holds(key(generate_key(an_a_nonce),a))),inference(cn,[status(thm)],[289,theory(equality)])). cnf(294,plain,(intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[68,282,theory(equality)])). cnf(295,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[140,282,theory(equality)])). cnf(296,plain,(intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),inference(spm,[status(thm)],[67,282,theory(equality)])). cnf(297,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),inference(spm,[status(thm)],[152,282,theory(equality)])). cnf(311,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(an_a_nonce)|~intruder_message(X1)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(X1)),inference(spm,[status(thm)],[229,296,theory(equality)])). cnf(315,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|$false|~intruder_message(X1)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(an_a_nonce)|~party_of_protocol(X1)),inference(rw,[status(thm)],[311,156,theory(equality)])). cnf(316,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|$false|~intruder_message(X1)|$false|~fresh_to_b(an_a_nonce)|~party_of_protocol(X1)),inference(rw,[status(thm)],[315,113,theory(equality)])). cnf(317,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|$false|~intruder_message(X1)|$false|$false|~party_of_protocol(X1)),inference(rw,[status(thm)],[316,46,theory(equality)])). cnf(318,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~party_of_protocol(X1)),inference(cn,[status(thm)],[317,theory(equality)])). cnf(331,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X1)|~party_of_protocol(X1)|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)))|~intruder_message(bt)),inference(spm,[status(thm)],[318,158,theory(equality)])). cnf(332,plain,(b_holds(key(generate_key(an_a_nonce),b))|~intruder_message(b)|~party_of_protocol(b)|~intruder_message(an_a_nonce)|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(spm,[status(thm)],[318,268,theory(equality)])). cnf(334,plain,(b_holds(key(generate_key(an_a_nonce),b))|$false|~party_of_protocol(b)|~intruder_message(an_a_nonce)|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[332,175,theory(equality)])). cnf(335,plain,(b_holds(key(generate_key(an_a_nonce),b))|$false|$false|~intruder_message(an_a_nonce)|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[334,45,theory(equality)])). cnf(336,plain,(b_holds(key(generate_key(an_a_nonce),b))|$false|$false|$false|~a_nonce(an_a_nonce)|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[335,156,theory(equality)])). cnf(337,plain,(b_holds(key(generate_key(an_a_nonce),b))|$false|$false|$false|$false|~fresh_to_b(an_a_nonce)),inference(rw,[status(thm)],[336,103,theory(equality)])). cnf(338,plain,(b_holds(key(generate_key(an_a_nonce),b))|$false|$false|$false|$false|$false),inference(rw,[status(thm)],[337,46,theory(equality)])). cnf(339,plain,(b_holds(key(generate_key(an_a_nonce),b))),inference(cn,[status(thm)],[338,theory(equality)])). cnf(344,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(triple(a,X3,encrypt(triple(a,X1,X2),at)))|~party_of_protocol(t)|~party_of_protocol(a)),inference(spm,[status(thm)],[228,96,theory(equality)])). cnf(345,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(triple(a,X3,encrypt(triple(a,X1,X2),at)))|$false|~party_of_protocol(a)),inference(rw,[status(thm)],[344,57,theory(equality)])). cnf(346,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(triple(a,X3,encrypt(triple(a,X1,X2),at)))|$false|$false),inference(rw,[status(thm)],[345,36,theory(equality)])). cnf(347,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(triple(a,X3,encrypt(triple(a,X1,X2),at)))),inference(cn,[status(thm)],[346,theory(equality)])). cnf(348,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~party_of_protocol(X1)),inference(csr,[status(thm)],[331,74])). cnf(349,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(a,X1,X2),bt))|~intruder_message(X3)|~intruder_message(b)),inference(spm,[status(thm)],[255,87,theory(equality)])). cnf(352,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(a,X1,X2),bt))|~intruder_message(X3)|$false),inference(rw,[status(thm)],[349,175,theory(equality)])). cnf(353,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(a,X1,X2),bt))|~intruder_message(X3)),inference(cn,[status(thm)],[352,theory(equality)])). cnf(360,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(X3)|~a_nonce(X1)|~intruder_message(triple(a,X1,X2))|~intruder_message(bt)),inference(spm,[status(thm)],[353,158,theory(equality)])). cnf(361,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1)))|~intruder_message(X1)|~a_nonce(an_a_nonce)),inference(spm,[status(thm)],[353,176,theory(equality)])). cnf(362,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~a_nonce(X1)|~intruder_message(X1)|~intruder_message(a)|~fresh_to_b(X1)|~party_of_protocol(a)),inference(spm,[status(thm)],[353,207,theory(equality)])). cnf(364,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1)))|~intruder_message(X1)|$false),inference(rw,[status(thm)],[361,103,theory(equality)])). cnf(365,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1)))|~intruder_message(X1)),inference(cn,[status(thm)],[364,theory(equality)])). cnf(366,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~a_nonce(X1)|~intruder_message(X1)|$false|~fresh_to_b(X1)|~party_of_protocol(a)),inference(rw,[status(thm)],[362,155,theory(equality)])). cnf(367,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~a_nonce(X1)|~intruder_message(X1)|$false|~fresh_to_b(X1)|$false),inference(rw,[status(thm)],[366,36,theory(equality)])). cnf(368,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~a_nonce(X1)|~intruder_message(X1)|~fresh_to_b(X1)),inference(cn,[status(thm)],[367,theory(equality)])). cnf(369,plain,(intruder_message(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at))),inference(spm,[status(thm)],[74,275,theory(equality)])). cnf(379,plain,(message(sent(a,b,pair(X1,encrypt(X2,generate_key(an_a_nonce)))))|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[192,369,theory(equality)])). cnf(381,plain,(intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[63,379,theory(equality)])). cnf(382,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(a)),inference(spm,[status(thm)],[51,379,theory(equality)])). cnf(384,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(a)),inference(spm,[status(thm)],[50,379,theory(equality)])). cnf(386,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|$false),inference(rw,[status(thm)],[382,155,theory(equality)])). cnf(387,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),inference(cn,[status(thm)],[386,theory(equality)])). cnf(393,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|$false),inference(rw,[status(thm)],[384,155,theory(equality)])). cnf(394,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),inference(cn,[status(thm)],[393,theory(equality)])). cnf(401,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|~a_key(generate_key(an_a_nonce))|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(generate_b_nonce(X2))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))),inference(spm,[status(thm)],[226,381,theory(equality)])). cnf(403,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X2,generate_key(an_a_nonce)))|~party_of_protocol(X1)|~intruder_message(X2)|~intruder_message(X1)),inference(spm,[status(thm)],[140,381,theory(equality)])). cnf(404,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[67,381,theory(equality)])). cnf(405,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(X2)|~intruder_message(X1)|~intruder_message(X2)),inference(spm,[status(thm)],[152,381,theory(equality)])). cnf(411,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|$false|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(generate_b_nonce(X2))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))),inference(rw,[status(thm)],[401,113,theory(equality)])). cnf(412,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(generate_b_nonce(X2))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))),inference(cn,[status(thm)],[411,theory(equality)])). cnf(420,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),inference(spm,[status(thm)],[404,275,theory(equality)])). cnf(452,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[394,122,theory(equality)])). cnf(453,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)|~party_of_protocol(X1)|~fresh_intruder_nonce(encrypt(X2,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[403,122,theory(equality)])). cnf(454,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)),inference(csr,[status(thm)],[412,208])). cnf(455,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)))|~intruder_message(bt)),inference(spm,[status(thm)],[454,158,theory(equality)])). cnf(456,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(generate_key(an_a_nonce))|~intruder_message(X1)|~fresh_to_b(generate_key(an_a_nonce))|~party_of_protocol(X1)),inference(spm,[status(thm)],[454,207,theory(equality)])). cnf(472,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[63,258,theory(equality)])). cnf(485,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)))|~intruder_message(bt)|~intruder_message(X2)|~fresh_to_b(X2)|~party_of_protocol(X1)),inference(csr,[status(thm)],[455,74])). cnf(487,plain,(intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[74,472,theory(equality)])). cnf(489,plain,(intruder_message(encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[73,472,theory(equality)])). cnf(503,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|~intruder_message(a)|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(a)|~a_nonce(X1)),inference(spm,[status(thm)],[231,489,theory(equality)])). cnf(513,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|$false|~intruder_message(generate_key(X1))|~a_key(generate_key(X1))|~fresh_to_b(X1)|~party_of_protocol(a)|~a_nonce(X1)),inference(rw,[status(thm)],[503,155,theory(equality)])). cnf(514,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|$false|~intruder_message(generate_key(X1))|$false|~fresh_to_b(X1)|~party_of_protocol(a)|~a_nonce(X1)),inference(rw,[status(thm)],[513,113,theory(equality)])). cnf(515,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|$false|~intruder_message(generate_key(X1))|$false|~fresh_to_b(X1)|$false|~a_nonce(X1)),inference(rw,[status(thm)],[514,36,theory(equality)])). cnf(516,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(X1)|~intruder_message(generate_key(X1))|~fresh_to_b(X1)|~a_nonce(X1)),inference(cn,[status(thm)],[515,theory(equality)])). cnf(542,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[63,265,theory(equality)])). cnf(548,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[387,122,theory(equality)])). cnf(549,plain,(intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1))|~intruder_message(X1)),inference(spm,[status(thm)],[63,365,theory(equality)])). cnf(551,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)))))|~intruder_message(X1)),inference(spm,[status(thm)],[146,365,theory(equality)])). cnf(553,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)),inference(spm,[status(thm)],[63,551,theory(equality)])). cnf(569,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)),inference(spm,[status(thm)],[140,553,theory(equality)])). cnf(571,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)),inference(spm,[status(thm)],[152,553,theory(equality)])). cnf(587,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(b,X1,X2),at))|~intruder_message(X3)|~intruder_message(a)),inference(spm,[status(thm)],[281,87,theory(equality)])). cnf(588,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(b,X1,X2),at))|~intruder_message(X3)|$false),inference(rw,[status(thm)],[587,155,theory(equality)])). cnf(589,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(b,X1,X2),at))|~intruder_message(X3)),inference(cn,[status(thm)],[588,theory(equality)])). cnf(598,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(X3)|~a_nonce(X1)|~intruder_message(triple(b,X1,X2))|~intruder_message(at)),inference(spm,[status(thm)],[589,158,theory(equality)])). cnf(599,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),inference(spm,[status(thm)],[295,122,theory(equality)])). cnf(600,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),inference(spm,[status(thm)],[297,122,theory(equality)])). cnf(601,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(a,X1,X2),at))|~intruder_message(X3)|~intruder_message(a)),inference(spm,[status(thm)],[347,87,theory(equality)])). cnf(602,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(a,X1,X2),at))|~intruder_message(X3)|$false),inference(rw,[status(thm)],[601,155,theory(equality)])). cnf(603,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~intruder_message(encrypt(triple(a,X1,X2),at))|~intruder_message(X3)),inference(cn,[status(thm)],[602,theory(equality)])). cnf(604,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(X3)|~a_nonce(X1)|~intruder_message(triple(a,X1,X2))|~intruder_message(at)),inference(spm,[status(thm)],[603,158,theory(equality)])). cnf(605,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X2)|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))),inference(spm,[status(thm)],[405,122,theory(equality)])). cnf(606,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),inference(spm,[status(thm)],[63,368,theory(equality)])). cnf(634,plain,(party_of_protocol(t)),57,['final']). cnf(635,plain,(party_of_protocol(a)),36,['final']). cnf(636,plain,(party_of_protocol(b)),45,['final']). cnf(637,plain,(fresh_to_b(an_a_nonce)),46,['final']). cnf(638,plain,(a_nonce(an_a_nonce)),103,['final']). cnf(639,plain,(fresh_intruder_nonce(an_intruder_nonce)),114,['final']). cnf(640,plain,(a_key(generate_key(X1))),113,['final']). cnf(641,plain,(a_nonce(generate_b_nonce(X1))),107,['final']). cnf(642,plain,(a_nonce(generate_expiration_time(X1))),108,['final']). cnf(643,plain,(a_holds(key(at,t))),35,['final']). cnf(644,plain,(a_stored(pair(b,an_a_nonce))),38,['final']). cnf(645,plain,(b_holds(key(bt,t))),44,['final']). cnf(646,plain,(t_holds(key(at,a))),55,['final']). cnf(647,plain,(t_holds(key(bt,b))),56,['final']). cnf(648,plain,(message(sent(a,b,pair(a,an_a_nonce)))),37,['final']). cnf(649,plain,(intruder_message(an_intruder_nonce)),123,['final']). cnf(650,plain,(intruder_message(pair(a,an_a_nonce))),126,['final']). cnf(651,plain,(intruder_message(a)),155,['final']). cnf(652,plain,(intruder_message(an_a_nonce)),156,['final']). cnf(653,plain,(b_stored(pair(a,an_a_nonce))),138,['final']). cnf(654,plain,(message(sent(b,t,triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))))),150,['final']). cnf(655,plain,(intruder_message(triple(b,generate_b_nonce(an_a_nonce),encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt)))),168,['final']). cnf(656,plain,(intruder_message(b)),175,['final']). cnf(657,plain,(intruder_message(generate_b_nonce(an_a_nonce))),177,['final']). cnf(658,plain,(intruder_message(encrypt(triple(a,an_a_nonce,generate_expiration_time(an_a_nonce)),bt))),176,['final']). cnf(659,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce))))),260,['final']). cnf(660,plain,(a_holds(key(generate_key(an_a_nonce),b))),276,['final']). cnf(661,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))))),277,['final']). cnf(662,plain,(b_holds(key(generate_key(an_a_nonce),a))),290,['final']). cnf(663,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))),282,['final']). cnf(664,plain,(intruder_message(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),296,['final']). cnf(665,plain,(intruder_message(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),294,['final']). cnf(666,plain,(b_holds(key(generate_key(an_a_nonce),b))),339,['final']). cnf(667,plain,(intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),generate_b_nonce(an_a_nonce)))),275,['final']). cnf(668,plain,(intruder_message(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at))),369,['final']). cnf(669,plain,(~a_nonce(generate_key(X1))),105,['final']). cnf(670,plain,(fresh_to_b(X1)|~fresh_intruder_nonce(X1)),122,['final']). cnf(671,plain,(intruder_message(X1)|~fresh_intruder_nonce(X1)),121,['final']). cnf(672,plain,(~a_nonce(X1)|~a_key(X1)),111,['final']). cnf(673,plain,(fresh_intruder_nonce(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),117,['final']). cnf(674,plain,(intruder_message(X1)|~intruder_message(pair(X2,X1))),67,['final']). cnf(675,plain,(intruder_message(X1)|~intruder_message(pair(X1,X2))),68,['final']). cnf(676,plain,(intruder_message(X1)|~intruder_message(triple(X2,X3,X1))),72,['final']). cnf(677,plain,(intruder_message(X1)|~intruder_message(triple(X2,X1,X3))),73,['final']). cnf(678,plain,(intruder_message(X1)|~message(sent(X2,X3,X1))),63,['final']). cnf(679,plain,(intruder_message(X1)|~intruder_message(triple(X1,X2,X3))),74,['final']). cnf(680,plain,(intruder_message(X1)|~intruder_message(quadruple(X2,X3,X4,X1))),78,['final']). cnf(681,plain,(intruder_message(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)),84,['final']). cnf(682,plain,(intruder_message(X1)|~intruder_message(quadruple(X2,X3,X1,X4))),79,['final']). cnf(683,plain,(intruder_message(X1)|~intruder_message(quadruple(X2,X1,X3,X4))),80,['final']). cnf(684,plain,(intruder_message(X1)|~intruder_message(quadruple(X1,X2,X3,X4))),81,['final']). cnf(685,plain,(intruder_holds(key(X1,X2))|~intruder_message(X1)|~party_of_protocol(X2)),99,['final']). cnf(686,plain,(message(sent(X1,X2,X3))|~intruder_message(X3)|~party_of_protocol(X2)|~party_of_protocol(X1)),96,['final']). cnf(687,plain,(intruder_message(triple(X1,X2,X3))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)),87,['final']). cnf(688,plain,(intruder_message(encrypt(X1,X2))|~intruder_holds(key(X2,X3))|~intruder_message(X1)|~party_of_protocol(X3)),102,['final']). cnf(689,plain,(intruder_message(X1)|~intruder_holds(key(X1,X2))|~intruder_message(encrypt(X3,X1))|~party_of_protocol(X2)),93,['final']). cnf(690,plain,(b_stored(pair(X1,X2))|~fresh_to_b(X2)|~message(sent(X1,b,pair(X1,X2)))),50,['final']). cnf(691,plain,(intruder_message(quadruple(X1,X2,X3,X4))|~intruder_message(X4)|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)),90,['final']). cnf(692,plain,(a_holds(key(X1,X2))|~a_stored(pair(X2,X3))|~message(sent(t,a,triple(encrypt(quadruple(X2,X3,X1,X4),at),X5,X6)))),42,['final']). cnf(693,plain,(message(sent(a,X1,pair(X2,encrypt(X3,X4))))|~a_stored(pair(X1,X5))|~message(sent(t,a,triple(encrypt(quadruple(X1,X5,X4,X6),at),X2,X3)))),43,['final']). cnf(694,plain,(b_holds(key(X1,X2))|~a_key(X1)|~b_stored(pair(X2,X3))|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))),54,['final']). cnf(695,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~fresh_to_b(X1)|~message(sent(X2,b,pair(X2,X1)))),51,['final']). cnf(696,plain,(message(sent(t,X1,triple(encrypt(quadruple(X2,X3,generate_key(X3),X4),X5),encrypt(triple(X1,generate_key(X3),X4),X6),X7)))|~a_nonce(X3)|~t_holds(key(X6,X2))|~t_holds(key(X5,X1))|~message(sent(X2,t,triple(X2,X7,encrypt(triple(X1,X3,X4),X6))))),60,['final']). cnf(697,plain,(intruder_message(generate_intruder_nonce(X1))|~fresh_intruder_nonce(X1)),125,['final']). cnf(698,plain,(intruder_message(encrypt(X1,X2))|~intruder_message(X1)|~intruder_message(X2)),158,['final']). cnf(699,plain,(b_stored(pair(X1,X2))|~intruder_message(pair(X1,X2))|~fresh_to_b(X2)|~party_of_protocol(X1)),140,['final']). cnf(700,plain,(b_stored(pair(X1,X2))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)),162,['final']). cnf(701,plain,(a_holds(key(X1,b))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4)))),145,['final']). cnf(702,plain,(a_holds(key(X1,b))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X1,X2),at),X3,X4))),172,['final']). cnf(703,plain,(a_holds(key(X1,b))|~intruder_message(encrypt(quadruple(b,an_a_nonce,X1,X2),at))|~intruder_message(X3)|~intruder_message(X4)),173,['final']). cnf(704,plain,(a_holds(key(X1,b))|~intruder_message(quadruple(b,an_a_nonce,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~intruder_message(X4)),174,['final']). cnf(705,plain,(b_holds(key(X1,a))|~a_key(X1)|~message(sent(a,b,pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1))))),157,['final']). cnf(706,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2)))),146,['final']). cnf(707,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(pair(X2,X1))|~fresh_to_b(X1)|~party_of_protocol(X2)),152,['final']). cnf(708,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(triple(encrypt(quadruple(b,an_a_nonce,X3,X4),at),X1,X2))),185,['final']). cnf(709,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(encrypt(quadruple(b,an_a_nonce,X3,X4),at))|~intruder_message(X2)|~intruder_message(X1)),192,['final']). cnf(710,plain,(message(sent(a,b,pair(X1,encrypt(X2,X3))))|~intruder_message(quadruple(b,an_a_nonce,X3,X4))|~intruder_message(at)|~intruder_message(X2)|~intruder_message(X1)),193,['final']). cnf(711,plain,(b_holds(key(X1,a))|~intruder_message(pair(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),X1)))|~a_key(X1)),181,['final']). cnf(712,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(encrypt(generate_b_nonce(an_a_nonce),X1))|~a_key(X1)),194,['final']). cnf(713,plain,(b_holds(key(X1,a))|~intruder_message(encrypt(triple(a,X1,generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~a_key(X1)),197,['final']). cnf(714,plain,(b_holds(key(an_a_nonce,a))|~a_key(an_a_nonce)),201,['final']). cnf(715,plain,(message(sent(t,X1,triple(encrypt(quadruple(b,X2,generate_key(X2),X3),X4),encrypt(triple(X1,generate_key(X2),X3),bt),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(b,t,triple(b,X5,encrypt(triple(X1,X2,X3),bt))))),153,['final']). cnf(716,plain,(b_holds(key(X1,a))|~intruder_message(triple(a,X1,generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~a_key(X1)),204,['final']). cnf(717,plain,(message(sent(b,t,triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)),187,['final']). cnf(718,plain,(intruder_message(triple(b,generate_b_nonce(X1),encrypt(triple(X2,X1,generate_expiration_time(X1)),bt)))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)),205,['final']). cnf(719,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(X1)|~party_of_protocol(X2)),208,['final']). cnf(720,plain,(intruder_message(encrypt(triple(X1,X2,generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)),207,['final']). cnf(721,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(b,X1,X2),bt))))),202,['final']). cnf(722,plain,(b_holds(key(X1,X2))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~message(sent(X2,b,pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1))))|~party_of_protocol(X2)),167,['final']). cnf(723,plain,(message(sent(t,X1,triple(encrypt(quadruple(a,X2,generate_key(X2),X3),X4),encrypt(triple(X1,generate_key(X2),X3),at),X5)))|~a_nonce(X2)|~t_holds(key(X4,X1))|~message(sent(a,t,triple(a,X5,encrypt(triple(X1,X2,X3),at))))),154,['final']). cnf(724,plain,(b_holds(key(X1,X2))|~intruder_message(pair(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt),encrypt(generate_b_nonce(X3),X1)))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),226,['final']). cnf(725,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(encrypt(generate_b_nonce(X3),X1))|~intruder_message(X3)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),229,['final']). cnf(726,plain,(b_holds(key(X1,X2))|~intruder_message(encrypt(triple(X2,X1,generate_expiration_time(X3)),bt))|~intruder_message(X3)|~intruder_message(X2)|~intruder_message(X1)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),231,['final']). cnf(727,plain,(b_holds(key(X1,X2))|~intruder_message(X1)|~intruder_message(X2)|~a_key(X1)|~fresh_to_b(X1)|~party_of_protocol(X2)),234,['final']). cnf(728,plain,(b_holds(key(X1,X2))|~intruder_message(triple(X2,X1,generate_expiration_time(X3)))|~intruder_message(bt)|~intruder_message(X3)|~a_key(X1)|~fresh_to_b(X3)|~party_of_protocol(X2)),241,['final']). cnf(729,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X3,encrypt(triple(b,X1,X2),bt)))|~a_nonce(X1)),220,['final']). cnf(730,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),223,['final']). cnf(731,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~a_nonce(X1)|~message(sent(b,t,triple(b,X3,encrypt(triple(a,X1,X2),bt))))),203,['final']). cnf(732,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(encrypt(triple(b,X1,X2),bt))|~intruder_message(X3)|~a_nonce(X1)),245,['final']). cnf(733,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X1,X2))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(X1)),261,['final']). cnf(734,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),249,['final']). cnf(735,plain,(intruder_message(generate_b_nonce(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),267,['final']). cnf(736,plain,(intruder_message(encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),268,['final']). cnf(737,plain,(b_holds(key(generate_key(X1),b))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),274,['final']). cnf(738,plain,(intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),266,['final']). cnf(739,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(b,X1,X2),at))))),227,['final']). cnf(740,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))|~intruder_message(X1)|~party_of_protocol(X1)),318,['final']). cnf(741,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~a_nonce(X1)|~message(sent(a,t,triple(a,X3,encrypt(triple(a,X1,X2),at))))),228,['final']). cnf(742,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)))|~intruder_message(bt)|~party_of_protocol(X1)),348,['final']). cnf(743,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(b,X3,encrypt(triple(a,X1,X2),bt)))|~a_nonce(X1)),255,['final']). cnf(744,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(encrypt(triple(a,X1,X2),bt))|~intruder_message(X3)|~a_nonce(X1)),353,['final']). cnf(745,plain,(message(sent(a,b,pair(X1,encrypt(X2,generate_key(an_a_nonce)))))|~intruder_message(X2)|~intruder_message(X1)),379,['final']). cnf(746,plain,(intruder_message(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)),381,['final']). cnf(747,plain,(intruder_message(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),420,['final']). cnf(748,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))),394,['final']). cnf(749,plain,(b_stored(pair(a,encrypt(X1,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),452,['final']). cnf(750,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(encrypt(X2,generate_key(an_a_nonce)))|~party_of_protocol(X1)),403,['final']). cnf(751,plain,(b_stored(pair(X1,encrypt(X2,generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(X2,generate_key(an_a_nonce)))|~intruder_message(X2)|~intruder_message(X1)|~party_of_protocol(X1)),453,['final']). cnf(752,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(encrypt(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)),bt))|~intruder_message(X2)|~intruder_message(X1)|~fresh_to_b(X2)|~party_of_protocol(X1)),454,['final']). cnf(753,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(generate_key(an_a_nonce))|~intruder_message(X1)|~fresh_to_b(generate_key(an_a_nonce))|~party_of_protocol(X1)),456,['final']). cnf(754,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1))))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),258,['final']). cnf(755,plain,(b_holds(key(generate_key(an_a_nonce),X1))|~intruder_message(triple(X1,generate_key(an_a_nonce),generate_expiration_time(X2)))|~intruder_message(bt)|~intruder_message(X2)|~fresh_to_b(X2)|~party_of_protocol(X1)),485,['final']). cnf(756,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),bt),X3)))|~intruder_message(triple(a,X1,X2))|~intruder_message(bt)|~intruder_message(X3)|~a_nonce(X1)),360,['final']). cnf(757,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),generate_b_nonce(X1)))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),472,['final']). cnf(758,plain,(intruder_message(encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),489,['final']). cnf(759,plain,(b_holds(key(generate_key(X1),a))|~intruder_message(generate_key(X1))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),516,['final']). cnf(760,plain,(intruder_message(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at))|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),487,['final']). cnf(761,plain,(message(sent(t,b,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),265,['final']). cnf(762,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),bt),encrypt(triple(b,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),542,['final']). cnf(763,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))),387,['final']). cnf(764,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(a,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)),548,['final']). cnf(765,plain,(message(sent(t,a,triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1)))|~intruder_message(X1)),365,['final']). cnf(766,plain,(message(sent(a,b,pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)))))|~intruder_message(X1)),551,['final']). cnf(767,plain,(intruder_message(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)),553,['final']). cnf(768,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X3,encrypt(triple(b,X1,X2),at)))|~a_nonce(X1)),281,['final']). cnf(769,plain,(intruder_message(triple(encrypt(quadruple(b,an_a_nonce,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),at),encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),X1))|~intruder_message(X1)),549,['final']). cnf(770,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(encrypt(triple(b,X1,X2),at))|~intruder_message(X3)|~a_nonce(X1)),589,['final']). cnf(771,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),295,['final']). cnf(772,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_to_b(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),297,['final']). cnf(773,plain,(message(sent(t,b,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),bt),encrypt(triple(b,generate_key(X1),X2),at),X3)))|~intruder_message(triple(b,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~a_nonce(X1)),598,['final']). cnf(774,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X3,encrypt(triple(a,X1,X2),at)))|~a_nonce(X1)),347,['final']). cnf(775,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(encrypt(triple(a,X1,X2),at))|~intruder_message(X3)|~a_nonce(X1)),603,['final']). cnf(776,plain,(message(sent(t,a,triple(encrypt(quadruple(a,X1,generate_key(X1),X2),at),encrypt(triple(a,generate_key(X1),X2),at),X3)))|~intruder_message(triple(a,X1,X2))|~intruder_message(at)|~intruder_message(X3)|~a_nonce(X1)),604,['final']). cnf(777,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),599,['final']). cnf(778,plain,(b_stored(pair(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),569,['final']). cnf(779,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~intruder_message(X2)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(X2)),405,['final']). cnf(780,plain,(message(sent(t,a,triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2)))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),368,['final']). cnf(781,plain,(intruder_message(triple(encrypt(quadruple(b,X1,generate_key(X1),generate_expiration_time(X1)),at),encrypt(triple(a,generate_key(X1),generate_expiration_time(X1)),bt),X2))|~intruder_message(X2)|~intruder_message(X1)|~a_nonce(X1)|~fresh_to_b(X1)),606,['final']). cnf(782,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(X2,encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(X1,generate_key(an_a_nonce)))|~intruder_message(X1)|~intruder_message(X2)|~party_of_protocol(X2)),605,['final']). cnf(783,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(X1,generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(X1,generate_key(an_a_nonce)),generate_expiration_time(encrypt(X1,generate_key(an_a_nonce)))),bt))))|~intruder_message(X1)|~fresh_to_b(encrypt(X1,generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),571,['final']). cnf(784,plain,(message(sent(b,t,triple(b,generate_b_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce))),encrypt(triple(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt),encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)),generate_expiration_time(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))),bt))))|~fresh_intruder_nonce(encrypt(generate_b_nonce(an_a_nonce),generate_key(an_a_nonce)))|~party_of_protocol(encrypt(triple(a,generate_key(an_a_nonce),generate_expiration_time(an_a_nonce)),bt))),600,['final']). # SZS output end Saturation.
# SZS status Theorem # SZS answers Tuple [[s__agent__m, s__experiencer__m]|_] # Proof found!
START OF MODEL (DIG): abstraction(esk1_0, esk3_0) act(esk1_0, esk5_0) actual_world(esk1_0) agent(esk1_0, esk5_0, esk2_0) animate(esk1_0, esk2_0) beverage(esk1_0, esk4_0) entity(esk1_0, esk4_0) entity(esk1_0, esk2_0) event(esk1_0, esk5_0) eventuality(esk1_0, esk5_0) existent(esk1_0, esk4_0) existent(esk1_0, esk2_0) female(esk1_0, esk2_0) food(esk1_0, esk4_0) forename(esk1_0, esk3_0) general(esk1_0, esk3_0) human(esk1_0, esk2_0) human_person(esk1_0, esk2_0) impartial(esk1_0, esk4_0) impartial(esk1_0, esk2_0) living(esk1_0, esk2_0) mia_forename(esk1_0, esk3_0) nonexistent(esk1_0, esk5_0) nonhuman(esk1_0, esk3_0) nonliving(esk1_0, esk4_0) nonreflexive(esk1_0, esk5_0) object(esk1_0, esk4_0) of(esk1_0, esk3_0, esk2_0) order(esk1_0, esk5_0) organism(esk1_0, esk2_0) past(esk1_0, esk5_0) patient(esk1_0, esk5_0, esk4_0) relation(esk1_0, esk3_0) relname(esk1_0, esk3_0) shake_beverage(esk1_0, esk4_0) singleton(esk1_0, esk4_0) singleton(esk1_0, esk5_0) singleton(esk1_0, esk2_0) singleton(esk1_0, esk3_0) specific(esk1_0, esk4_0) specific(esk1_0, esk5_0) specific(esk1_0, esk2_0) substance_matter(esk1_0, esk4_0) thing(esk1_0, esk4_0) thing(esk1_0, esk5_0) thing(esk1_0, esk2_0) thing(esk1_0, esk3_0) unisex(esk1_0, esk4_0) unisex(esk1_0, esk5_0) unisex(esk1_0, esk3_0) woman(esk1_0, esk2_0) END OF MODEL
% SZS status Theorem % SZS answers Tuple [[s__agent__m,s__experiencer__m]].
# Preprocessing time : 0.012 s # Problem is unsatisfiable (or provable), constructing proof object # SZS status Theorem # SZS output start CNFRefutation. fof(8, axiom,![X1]:![X2]:(subset(X1,X2)<=>![X3]:(in(X3,X1)=>in(X3,X2))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', d3_tarski)). fof(27, axiom,![X1]:![X2]:(disjoint(X1,X2)=>disjoint(X2,X1)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', symmetry_r1_xboole_0)). fof(43, axiom,![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', t3_xboole_0)). fof(51, conjecture,![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3)),file('/Users/schulz/EPROVER/TPTP_4.1.0_FLAT/SEU140+2.p', t63_xboole_1)). fof(57, negated_conjecture,~(![X1]:![X2]:![X3]:((subset(X1,X2)&disjoint(X2,X3))=>disjoint(X1,X3))),inference(assume_negation,[status(cth)],[51])). fof(66, plain,![X1]:![X2]:(~((~(disjoint(X1,X2))&![X3]:~((in(X3,X1)&in(X3,X2)))))&~((?[X3]:(in(X3,X1)&in(X3,X2))&disjoint(X1,X2)))),inference(fof_simplification,[status(thm)],[43,theory(equality)])). fof(101, plain,![X1]:![X2]:((~(subset(X1,X2))|![X3]:(~(in(X3,X1))|in(X3,X2)))&(?[X3]:(in(X3,X1)&~(in(X3,X2)))|subset(X1,X2))),inference(fof_nnf,[status(thm)],[8])). fof(102, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&(?[X7]:(in(X7,X4)&~(in(X7,X5)))|subset(X4,X5))),inference(variable_rename,[status(thm)],[101])). fof(103, plain,![X4]:![X5]:((~(subset(X4,X5))|![X6]:(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)&~(in(esk3_2(X4,X5),X5)))|subset(X4,X5))),inference(skolemize,[status(esa)],[102])). fof(104, plain,![X4]:![X5]:![X6]:((~(subset(X4,X5))|(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)&~(in(esk3_2(X4,X5),X5)))|subset(X4,X5))),inference(shift_quantors,[status(thm)],[103])). fof(105, plain,![X4]:![X5]:![X6]:((~(subset(X4,X5))|(~(in(X6,X4))|in(X6,X5)))&((in(esk3_2(X4,X5),X4)|subset(X4,X5))&(~(in(esk3_2(X4,X5),X5))|subset(X4,X5)))),inference(distribute,[status(thm)],[104])). cnf(108,plain,(in(X1,X2)|~in(X1,X3)|~subset(X3,X2)),inference(split_conjunct,[status(thm)],[105])). fof(170, plain,![X1]:![X2]:(~(disjoint(X1,X2))|disjoint(X2,X1)),inference(fof_nnf,[status(thm)],[27])). fof(171, plain,![X3]:![X4]:(~(disjoint(X3,X4))|disjoint(X4,X3)),inference(variable_rename,[status(thm)],[170])). cnf(172,plain,(disjoint(X1,X2)|~disjoint(X2,X1)),inference(split_conjunct,[status(thm)],[171])). fof(215, plain,![X1]:![X2]:((disjoint(X1,X2)|?[X3]:(in(X3,X1)&in(X3,X2)))&(![X3]:(~(in(X3,X1))|~(in(X3,X2)))|~(disjoint(X1,X2)))),inference(fof_nnf,[status(thm)],[66])). fof(216, plain,![X4]:![X5]:((disjoint(X4,X5)|?[X6]:(in(X6,X4)&in(X6,X5)))&(![X7]:(~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(variable_rename,[status(thm)],[215])). fof(217, plain,![X4]:![X5]:((disjoint(X4,X5)|(in(esk9_2(X4,X5),X4)&in(esk9_2(X4,X5),X5)))&(![X7]:(~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(skolemize,[status(esa)],[216])). fof(218, plain,![X4]:![X5]:![X7]:((disjoint(X4,X5)|(in(esk9_2(X4,X5),X4)&in(esk9_2(X4,X5),X5)))&((~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(shift_quantors,[status(thm)],[217])). fof(219, plain,![X4]:![X5]:![X7]:(((in(esk9_2(X4,X5),X4)|disjoint(X4,X5))&(in(esk9_2(X4,X5),X5)|disjoint(X4,X5)))&((~(in(X7,X4))|~(in(X7,X5)))|~(disjoint(X4,X5)))),inference(distribute,[status(thm)],[218])). cnf(220,plain,(~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1)),inference(split_conjunct,[status(thm)],[219])). cnf(221,plain,(disjoint(X1,X2)|in(esk9_2(X1,X2),X2)),inference(split_conjunct,[status(thm)],[219])). cnf(222,plain,(disjoint(X1,X2)|in(esk9_2(X1,X2),X1)),inference(split_conjunct,[status(thm)],[219])). fof(244, negated_conjecture,?[X1]:?[X2]:?[X3]:((subset(X1,X2)&disjoint(X2,X3))&~(disjoint(X1,X3))),inference(fof_nnf,[status(thm)],[57])). fof(245, negated_conjecture,?[X4]:?[X5]:?[X6]:((subset(X4,X5)&disjoint(X5,X6))&~(disjoint(X4,X6))),inference(variable_rename,[status(thm)],[244])). fof(246, negated_conjecture,((subset(esk11_0,esk12_0)&disjoint(esk12_0,esk13_0))&~(disjoint(esk11_0,esk13_0))),inference(skolemize,[status(esa)],[245])). cnf(247,negated_conjecture,(~disjoint(esk11_0,esk13_0)),inference(split_conjunct,[status(thm)],[246])). cnf(248,negated_conjecture,(disjoint(esk12_0,esk13_0)),inference(split_conjunct,[status(thm)],[246])). cnf(249,negated_conjecture,(subset(esk11_0,esk12_0)),inference(split_conjunct,[status(thm)],[246])). cnf(384,plain,(disjoint(X1,X2)|in(esk9_2(X2,X1),X1)),inference(spm,[status(thm)],[172,221,theory(equality)])). cnf(386,plain,(disjoint(X1,X2)|in(esk9_2(X2,X1),X2)),inference(spm,[status(thm)],[172,222,theory(equality)])). cnf(474,negated_conjecture,(in(X1,esk12_0)|~in(X1,esk11_0)),inference(spm,[status(thm)],[108,249,theory(equality)])). cnf(485,negated_conjecture,(~in(X1,esk13_0)|~in(X1,esk12_0)),inference(spm,[status(thm)],[220,248,theory(equality)])). cnf(2151,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk11_0)),inference(spm,[status(thm)],[247,384,theory(equality)])). cnf(2160,negated_conjecture,(in(esk9_2(esk13_0,esk11_0),esk13_0)),inference(spm,[status(thm)],[247,386,theory(equality)])). cnf(2169,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk12_0)),inference(spm,[status(thm)],[485,2160,theory(equality)])). cnf(2622,negated_conjecture,(~in(esk9_2(esk13_0,esk11_0),esk11_0)),inference(spm,[status(thm)],[2169,474,theory(equality)])). cnf(2640,negated_conjecture,($false),inference(rw,[status(thm)],[2622,2151,theory(equality)])). cnf(2641,negated_conjecture,($false),inference(cn,[status(thm)],[2640,theory(equality)])). cnf(2642,negated_conjecture,($false),2641,['proof']). # SZS output end CNFRefutation
finite domain: {1,2,3,4} esk2_0 = 1 esk3_0 = 2 esk4_0 = 3 esk5_0 = 4 esk1_0 = 1 abstraction/2: (1,2) <=> True (X1,X2) <=> abstraction(1,X2) : X1>1 impartial/2: (X0,X1) <=> True *p* woman/2: (1,1) <=> True (X1,X2) <=> woman(1,X2) : X1>1 act/2: (1,4) <=> True (X1,X2) <=> act(1,X2) : X1>1 animate/2: (1,1) <=> True (X1,X2) <=> animate(1,X2) : X1>1 thing/2: (X0,X1) <=> True *p* organism/2: (1,1) <=> True (X1,X2) <=> organism(1,X2) : X1>1 relname/2: (1,2) <=> True (X1,X2) <=> relname(1,X2) : X1>1 nonexistent/2: (1,4) <=> True (X1,X2) <=> nonexistent(1,X2) : X1>1 general/2: (1,2) <=> True (X1,X2) <=> general(1,X2) : X1>1 food/2: (1,3) <=> True (X1,X2) <=> food(1,X2) : X1>1 female/2: (1,1) <=> True (X1,X2) <=> female(1,X2) : X1>1 shake_beverage/2: (1,3) <=> True (X1,X2) <=> shake_beverage(1,X2) : X1>1 of/3: (1,2,1) <=> True (X1,X2,X3) <=> of(1,X2,X3) : X1>1 forename/2: (1,2) <=> True (X1,X2) <=> forename(1,X2) : X1>1 beverage/2: (1,3) <=> True (X1,X2) <=> beverage(1,X2) : X1>1 order/2: (1,4) <=> True (X1,X2) <=> order(1,X2) : X1>1 existent/2: (1,1) <=> True (1,2) <=> True (1,3) <=> True (X1,X2) <=> existent(1,X2) : X1>1 nonreflexive/2: (1,4) <=> True (X1,X2) <=> nonreflexive(1,X2) : X1>1 singleton/2: (X0,X1) <=> True *p* living/2: (1,1) <=> True (X1,X2) <=> living(1,X2) : X1>1 specific/2: (1,1) <=> True (1,3) <=> True (1,4) <=> True (X1,X2) <=> specific(1,X2) : X1>1 patient/3: (1,4,3) <=> True (X1,X2,X3) <=> patient(1,X2,X3) : X1>1 actual_world/1: (X0) <=> True *p* object/2: (1,3) <=> True (X1,X2) <=> object(1,X2) : X1>1 past/2: (X0,X1) <=> True *p* agent/3: (1,4,1) <=> True (X1,X2,X3) <=> agent(1,X2,X3) : X1>1 human/2: (1,1) <=> True (X1,X2) <=> human(1,X2) : X1>1 event/2: (1,4) <=> True (X1,X2) <=> event(1,X2) : X1>1 nonliving/2: (1,2) <=> True (1,3) <=> True (1,4) <=> True (X1,X2) <=> nonliving(1,X2) : X1>1 human_person/2: (1,1) <=> True (X1,X2) <=> human_person(1,X2) : X1>1 eventuality/2: (1,4) <=> True (X1,X2) <=> eventuality(1,X2) : X1>1 unisex/2: (1,2) <=> True (1,3) <=> True (1,4) <=> True (X1,X2) <=> unisex(1,X2) : X1>1 entity/2: (1,1) <=> True (1,3) <=> True (X1,X2) <=> entity(1,X2) : X1>1 relation/2: (1,2) <=> True (X1,X2) <=> relation(1,X2) : X1>1 nonhuman/2: (1,2) <=> True (1,3) <=> True (1,4) <=> True (X1,X2) <=> nonhuman(1,X2) : X1>1 mia_forename/2: (1,2) <=> True (X1,X2) <=> mia_forename(1,X2) : X1>1 substance_matter/2: (1,3) <=> True (X1,X2) <=> substance_matter(1,X2) : X1>1
finite domain: {1,2} a = 1 b = 1 bt = 1 an_intruder_nonce = 2 t = 1 an_a_nonce = 2 at = 2 triple/3: (1,1,1) = 1 (1,1,2) = 2 (1,2,2) = 2 (2,1,1) = 2 (2,1,2) = 2 (2,2,1) = 2 (1,2,1) = 1 (2,2,2) = 1 generate_expiration_time/1: (2) = 2 (1) = 2 key/2: (2,1) = 2 (1,1) = 2 (1,2) = 1 (2,2) = 1 generate_intruder_nonce/1: (1) = 1 (2) = 2 sent/3: (1,1,2) = 2 (1,2,1) = 2 (1,2,2) = 2 (2,1,1) = 2 (2,1,2) = 2 (2,2,1) = 2 (1,1,1) = 2 (2,2,2) = 1 quadruple/4: (1,1,1,2) = 2 (1,2,1,1) = 2 (1,2,1,2) = 2 (2,1,1,1) = 2 (2,1,1,2) = 2 (2,2,1,1) = 2 (2,2,1,2) = 2 (1,1,2,1) = 2 (1,1,2,2) = 2 (1,2,2,1) = 2 (1,2,2,2) = 2 (2,2,2,1) = 2 (2,2,2,2) = 2 (1,1,1,1) = 2 (2,1,2,1) = 1 (2,1,2,2) = 1 generate_b_nonce/1: (2) = 2 (1) = 2 generate_key/1: (1) = 1 (2) = 1 encrypt/2: (1,1) = 1 (2,2) = 2 (2,1) = 1 (1,2) = 1 pair/2: (2,1) = 2 (1,2) = 2 (2,2) = 2 (1,1) = 2 t_holds/1: (2) <=> True a_holds/1: (X0) <=> True *p* message/1: (2) <=> True b_stored/1: (X0) <=> True *p* intruder_message/1: (1) <=> True (2) <=> True fresh_intruder_nonce/1: (2) <=> True a_key/1: (1) <=> True b_holds/1: (X0) <=> True *p* a_nonce/1: (2) <=> True a_stored/1: (2) <=> True intruder_holds/1: (2) <=> True fresh_to_b/1: (2) <=> True party_of_protocol/1: (1) <=> True
% SZS output start Model %------ Negative definition of $equality_sorted fof(lit_def,axiom, (! [X0,X1,X2] : ( ~($equality_sorted(X0,X1,X2)) <=> ( ( ( X0=$i & X1=sK2 ) & ( X2!=sK2 ) ) | ( ( X0=$i & X1=sK1 ) & ( X2!=sK1 ) ) | ( ( X0=$i & X1=sK3 ) & ( X2!=sK3 ) ) | ( ( X0=$i & X1=sK4 ) & ( X2!=sK4 ) ) | ( ( X0=$i & X2=sK2 ) & ( X1!=sK2 ) ) | ( ( X0=$i & X2=sK1 ) & ( X1!=sK1 ) ) | ( ( X0=$i & X2=sK3 ) & ( X1!=sK3 ) ) | ( ( X0=$i & X2=sK4 ) & ( X1!=sK4 ) ) ) ) ) ). %------ Positive definition of female fof(lit_def,axiom, (! [X0,X1] : ( female(X0,X1) <=> ( ( ( X0=sK0 & X1=sK1 ) ) | ( ( X1=sK1 ) ) ) ) ) ). %------ Positive definition of woman fof(lit_def,axiom, (! [X0,X1] : ( woman(X0,X1) <=> ( ( ( X0=sK0 & X1=sK1 ) ) | ( ( X1=sK1 ) ) ) ) ) ). %------ Positive definition of animate fof(lit_def,axiom, (! [X0,X1] : ( animate(X0,X1) <=> ( ( ( X0=sK0 & X1=sK1 ) ) | ( ( X1=sK1 ) ) ) ) ) ). %------ Positive definition of human_person fof(lit_def,axiom, (! [X0,X1] : ( human_person(X0,X1) <=> ( ( ( X0=sK0 & X1=sK1 ) ) | ( ( X1=sK1 ) ) ) ) ) ). %------ Positive definition of human fof(lit_def,axiom, (! [X0,X1] : ( human(X0,X1) <=> ( ( ( X0=sK0 & X1=sK1 ) ) | ( ( X1=sK1 ) ) ) ) ) ). %------ Positive definition of living fof(lit_def,axiom, (! [X0,X1] : ( living(X0,X1) <=> ( ( ( X0=sK0 & X1=sK1 ) ) | ( ( X1=sK1 ) ) ) ) ) ). %------ Positive definition of organism fof(lit_def,axiom, (! [X0,X1] : ( organism(X0,X1) <=> ( ( ( X0=sK0 & X1=sK1 ) ) | ( ( X1=sK1 ) ) ) ) ) ). %------ Positive definition of entity fof(lit_def,axiom, (! [X0,X1] : ( entity(X0,X1) <=> ( ( ( X0=sK0 & X1=sK1 ) ) | ( ( X0=sK0 & X1=sK3 ) ) | ( ( X1=sK1 ) ) | ( ( X1=sK3 ) ) ) ) ) ). %------ Positive definition of forename fof(lit_def,axiom, (! [X0,X1] : ( forename(X0,X1) <=> ( ( ( X0=sK0 & X1=sK2 ) ) | ( ( X1=sK2 ) & ( X0!=sK0 ) ) ) ) ) ). %------ Positive definition of mia_forename fof(lit_def,axiom, (! [X0,X1] : ( mia_forename(X0,X1) <=> ( ( ( X0=sK0 & X1=sK2 ) ) | ( ( X1=sK2 ) ) ) ) ) ). %------ Positive definition of unisex fof(lit_def,axiom, (! [X0,X1] : ( unisex(X0,X1) <=> ( ( ( X0=sK0 & X1=sK2 ) ) | ( ( X0=sK0 & X1=sK3 ) ) | ( ( X0=sK0 & X1=sK4 ) ) | ( ( X1=sK2 ) ) | ( ( X1=sK3 ) ) | ( ( X1=sK4 ) ) ) ) ) ). %------ Positive definition of abstraction fof(lit_def,axiom, (! [X0,X1] : ( abstraction(X0,X1) <=> ( ( ( X0=sK0 & X1=sK2 ) ) | ( ( X1=sK2 ) ) ) ) ) ). %------ Positive definition of general fof(lit_def,axiom, (! [X0,X1] : ( general(X0,X1) <=> ( ( ( X0=sK0 & X1=sK2 ) ) | ( ( X1=sK2 ) ) ) ) ) ). %------ Positive definition of nonhuman fof(lit_def,axiom, (! [X0,X1] : ( nonhuman(X0,X1) <=> ( ( ( X0=sK0 & X1=sK2 ) ) | ( ( X1=sK2 ) ) ) ) ) ). %------ Positive definition of relation fof(lit_def,axiom, (! [X0,X1] : ( relation(X0,X1) <=> ( ( ( X0=sK0 & X1=sK2 ) ) | ( ( X1=sK2 ) ) ) ) ) ). %------ Positive definition of relname fof(lit_def,axiom, (! [X0,X1] : ( relname(X0,X1) <=> ( ( ( X0=sK0 & X1=sK2 ) ) | ( ( X1=sK2 ) ) ) ) ) ). %------ Positive definition of object fof(lit_def,axiom, (! [X0,X1] : ( object(X0,X1) <=> ( ( ( X0=sK0 & X1=sK3 ) ) | ( ( X1=sK3 ) ) ) ) ) ). %------ Positive definition of nonliving fof(lit_def,axiom, (! [X0,X1] : ( nonliving(X0,X1) <=> ( ( ( X0=sK0 & X1=sK3 ) ) | ( ( X1=sK3 ) ) ) ) ) ). %------ Positive definition of existent fof(lit_def,axiom, (! [X0,X1] : ( existent(X0,X1) <=> ( ( ( X0=sK0 & X1=sK1 ) ) | ( ( X0=sK0 & X1=sK3 ) ) | ( ( X1=sK1 ) ) | ( ( X1=sK3 ) ) ) ) ) ). %------ Positive definition of specific fof(lit_def,axiom, (! [X0,X1] : ( specific(X0,X1) <=> ( ( ( X0=sK0 & X1=sK1 ) ) | ( ( X0=sK0 & X1=sK3 ) ) | ( ( X0=sK0 & X1=sK4 ) ) | ( ( X1=sK1 ) ) | ( ( X1=sK3 ) ) | ( ( X1=sK4 ) ) ) ) ) ). %------ Positive definition of substance_matter fof(lit_def,axiom, (! [X0,X1] : ( substance_matter(X0,X1) <=> ( ( ( X0=sK0 & X1=sK3 ) ) | ( ( X1=sK3 ) ) ) ) ) ). %------ Positive definition of food fof(lit_def,axiom, (! [X0,X1] : ( food(X0,X1) <=> ( ( ( X0=sK0 & X1=sK3 ) ) | ( ( X1=sK3 ) ) ) ) ) ). %------ Positive definition of beverage fof(lit_def,axiom, (! [X0,X1] : ( beverage(X0,X1) <=> ( ( ( X0=sK0 & X1=sK3 ) ) | ( ( X1=sK3 ) ) ) ) ) ). %------ Positive definition of shake_beverage fof(lit_def,axiom, (! [X0,X1] : ( shake_beverage(X0,X1) <=> ( ( ( X0=sK0 & X1=sK3 ) ) | ( ( X1=sK3 ) ) ) ) ) ). %------ Positive definition of event fof(lit_def,axiom, (! [X0,X1] : ( event(X0,X1) <=> ( ( ( X0=sK0 & X1=sK4 ) ) | ( ( X1=sK4 ) ) ) ) ) ). %------ Positive definition of order fof(lit_def,axiom, (! [X0,X1] : ( order(X0,X1) <=> ( ( ( X0=sK0 & X1=sK4 ) ) | ( ( X1=sK4 ) ) ) ) ) ). %------ Positive definition of eventuality fof(lit_def,axiom, (! [X0,X1] : ( eventuality(X0,X1) <=> ( ( ( X0=sK0 & X1=sK4 ) ) | ( ( X1=sK4 ) ) ) ) ) ). %------ Positive definition of nonexistent fof(lit_def,axiom, (! [X0,X1] : ( nonexistent(X0,X1) <=> ( ( ( X0=sK0 & X1=sK4 ) ) | ( ( X1=sK4 ) ) ) ) ) ). %------ Positive definition of act fof(lit_def,axiom, (! [X0,X1] : ( act(X0,X1) <=> ( ( ( X0=sK0 & X1=sK4 ) ) | ( ( X1=sK4 ) ) ) ) ) ). %------ Positive definition of of fof(lit_def,axiom, (! [X0,X1,X2] : ( of(X0,X1,X2) <=> ( ( ( X0=sK0 & X1=sK2 & X2=sK1 ) ) | ( ( X1=sK2 & X2=sK1 ) ) ) ) ) ). %------ Positive definition of nonreflexive fof(lit_def,axiom, (! [X0,X1] : ( nonreflexive(X0,X1) <=> ( ( ( X0=sK0 & X1=sK4 ) ) | ( ( X1=sK4 ) ) ) ) ) ). %------ Positive definition of agent fof(lit_def,axiom, (! [X0,X1,X2] : ( agent(X0,X1,X2) <=> ( ( ( X0=sK0 & X1=sK4 & X2=sK1 ) ) | ( ( X1=sK4 & X2=sK1 ) ) ) ) ) ). %------ Positive definition of patient fof(lit_def,axiom, (! [X0,X1,X2] : ( patient(X0,X1,X2) <=> ( ( ( X0=sK0 & X1=sK4 & X2=sK3 ) ) | ( ( X1=sK4 & X2=sK3 ) ) ) ) ) ). % SZS output end Model
% SZS output start Model %------ Positive definition of $equality_sorted fof(lit_def,axiom, (! [X0,X1,X2] : ( $equality_sorted(X0,X1,X2) <=> $false ) ) ). %------ Negative definition of party_of_protocol fof(lit_def,axiom, (! [X0] : ( ~(party_of_protocol(X0)) <=> $false ) ) ). %------ Positive definition of message fof(lit_def,axiom, (! [X0] : ( message(X0) <=> ( ( ( X0=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of a_stored fof(lit_def,axiom, (! [X0] : ( a_stored(X0) <=> ( ( ( X0=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of fresh_to_b fof(lit_def,axiom, (! [X0] : ( fresh_to_b(X0) <=> ( ( ( X0=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 ) ) ) ) ) ). %------ Positive definition of t_holds fof(lit_def,axiom, (! [X0] : ( t_holds(X0) <=> ( ( ( X0=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of a_nonce fof(lit_def,axiom, (! [X0] : ( a_nonce(X0) <=> ( ( ( X0=iProver_Domain_2 ) ) ) ) ) ). %------ Negative definition of intruder_message fof(lit_def,axiom, (! [X0] : ( ~(intruder_message(X0)) <=> $false ) ) ). %------ Positive definition of intruder_holds fof(lit_def,axiom, (! [X0] : ( intruder_holds(X0) <=> ( ( ( X0=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of a_key fof(lit_def,axiom, (! [X0] : ( a_key(X0) <=> ( ( ( X0=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of fresh_intruder_nonce fof(lit_def,axiom, (! [X0] : ( fresh_intruder_nonce(X0) <=> ( ( ( X0=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_a fof(lit_def,axiom, (! [X0] : ( iProver_Flat_a(X0) <=> ( ( ( X0=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_an_a_nonce fof(lit_def,axiom, (! [X0] : ( iProver_Flat_an_a_nonce(X0) <=> ( ( ( X0=iProver_Domain_2 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_an_intruder_nonce fof(lit_def,axiom, (! [X0] : ( iProver_Flat_an_intruder_nonce(X0) <=> ( ( ( X0=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_at fof(lit_def,axiom, (! [X0] : ( iProver_Flat_at(X0) <=> ( ( ( X0=iProver_Domain_2 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_b fof(lit_def,axiom, (! [X0] : ( iProver_Flat_b(X0) <=> ( ( ( X0=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_bt fof(lit_def,axiom, (! [X0] : ( iProver_Flat_bt(X0) <=> ( ( ( X0=iProver_Domain_2 ) ) ) ) ) ). %------ Negative definition of iProver_Flat_encrypt fof(lit_def,axiom, (! [X0,X1,X2] : ( ~(iProver_Flat_encrypt(X0,X1,X2)) <=> ( ( ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X2!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 | X2!=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_1 & X2=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_2 ) & ( X2!=iProver_Domain_2 ) ) | ( ( X1=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X2!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 | X2!=iProver_Domain_2 ) ) | ( ( X1=iProver_Domain_2 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 | X2!=iProver_Domain_2 ) ) | ( ( X2=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) ) | ( ( X2=iProver_Domain_2 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_generate_b_nonce fof(lit_def,axiom, (! [X0,X1] : ( iProver_Flat_generate_b_nonce(X0,X1) <=> ( ( ( X0=iProver_Domain_2 ) & ( X1!=iProver_Domain_1 ) & ( X1!=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_2 & X1=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 & X1=iProver_Domain_2 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_generate_expiration_time fof(lit_def,axiom, (! [X0,X1] : ( iProver_Flat_generate_expiration_time(X0,X1) <=> ( ( ( X0=iProver_Domain_2 ) & ( X1!=iProver_Domain_1 ) & ( X1!=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_2 & X1=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 & X1=iProver_Domain_2 ) ) ) ) ) ). %------ Negative definition of iProver_Flat_generate_intruder_nonce fof(lit_def,axiom, (! [X0,X1] : ( ~(iProver_Flat_generate_intruder_nonce(X0,X1)) <=> ( ( ( X1=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_generate_key fof(lit_def,axiom, (! [X0,X1] : ( iProver_Flat_generate_key(X0,X1) <=> ( ( ( X0=iProver_Domain_1 ) & ( X1!=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_1 & X1=iProver_Domain_2 ) ) ) ) ) ). %------ Negative definition of iProver_Flat_key fof(lit_def,axiom, (! [X0,X1,X2] : ( ~(iProver_Flat_key(X0,X1,X2)) <=> ( ( ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X1!=iProver_Domain_1 ) & ( X1!=iProver_Domain_1 ) ) | ( ( X1=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) ) | ( ( X1=iProver_Domain_1 & X2=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) ) | ( ( X1=iProver_Domain_2 & X2=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_pair fof(lit_def,axiom, (! [X0,X1,X2] : ( iProver_Flat_pair(X0,X1,X2) <=> ( ( ( X0=iProver_Domain_1 & X1=iProver_Domain_1 ) & ( X2!=iProver_Domain_1 ) & ( X2!=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_1 & X2=iProver_Domain_1 ) & ( X1!=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_1 & X2=iProver_Domain_2 ) & ( X1!=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 ) & ( X1!=iProver_Domain_1 ) & ( X1!=iProver_Domain_1 | X2!=iProver_Domain_1 ) & ( X1!=iProver_Domain_1 | X2!=iProver_Domain_2 ) & ( X2!=iProver_Domain_1 ) & ( X2!=iProver_Domain_2 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_quadruple fof(lit_def,axiom, (! [X0,X1,X2,X3,X4] : ( iProver_Flat_quadruple(X0,X1,X2,X3,X4) <=> ( ( ( X0=iProver_Domain_1 & X1=iProver_Domain_1 ) & ( X2!=iProver_Domain_2 | X3!=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_2 & X3=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_2 & X3=iProver_Domain_1 & X4=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_1 & X1=iProver_Domain_2 & X2=iProver_Domain_2 & X3=iProver_Domain_1 & X4=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_1 & X2=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_1 & X3=iProver_Domain_1 ) & ( X1!=iProver_Domain_1 | X2!=iProver_Domain_2 ) & ( X1!=iProver_Domain_2 | X2!=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_1 & X4=iProver_Domain_1 ) & ( X1!=iProver_Domain_1 | X2!=iProver_Domain_2 | X3!=iProver_Domain_1 ) & ( X1!=iProver_Domain_2 | X2!=iProver_Domain_2 | X3!=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 ) & ( X1!=iProver_Domain_1 ) & ( X1!=iProver_Domain_1 | X2!=iProver_Domain_2 | X3!=iProver_Domain_1 ) & ( X2!=iProver_Domain_1 ) & ( X3!=iProver_Domain_1 ) & ( X4!=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 & X1=iProver_Domain_2 & X2=iProver_Domain_2 & X3=iProver_Domain_1 ) & ( X4!=iProver_Domain_1 ) ) ) ) ) ). %------ Negative definition of iProver_Flat_sent fof(lit_def,axiom, (! [X0,X1,X2,X3] : ( ~(iProver_Flat_sent(X0,X1,X2,X3)) <=> ( ( ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X3!=iProver_Domain_1 ) & ( X3!=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 & X1=iProver_Domain_1 & X2=iProver_Domain_1 & X3=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 & X2=iProver_Domain_1 & X3=iProver_Domain_1 ) ) | ( ( X1=iProver_Domain_1 & X2=iProver_Domain_1 & X3=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 ) ) | ( ( X1=iProver_Domain_1 & X3=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X2!=iProver_Domain_1 ) ) | ( ( X1=iProver_Domain_1 & X3=iProver_Domain_2 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X2!=iProver_Domain_1 ) ) | ( ( X3=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 | X2!=iProver_Domain_1 ) ) ) ) ) ). %------ Positive definition of iProver_Flat_t fof(lit_def,axiom, (! [X0] : ( iProver_Flat_t(X0) <=> ( ( ( X0=iProver_Domain_1 ) ) ) ) ) ). %------ Negative definition of iProver_Flat_triple fof(lit_def,axiom, (! [X0,X1,X2,X3] : ( ~(iProver_Flat_triple(X0,X1,X2,X3)) <=> ( ( ( X0=iProver_Domain_1 ) & ( X1!=iProver_Domain_1 ) & ( X1!=iProver_Domain_2 ) & ( X2!=iProver_Domain_1 ) & ( X3!=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_1 ) & ( X3!=iProver_Domain_1 ) & ( X3!=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_1 & X1=iProver_Domain_1 & X2=iProver_Domain_2 ) & ( X3!=iProver_Domain_1 ) & ( X3!=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_1 & X2=iProver_Domain_1 & X3=iProver_Domain_1 ) & ( X1!=iProver_Domain_1 ) & ( X1!=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_1 & X3=iProver_Domain_2 ) & ( X1!=iProver_Domain_1 ) & ( X1!=iProver_Domain_1 | X2!=iProver_Domain_1 ) & ( X1!=iProver_Domain_1 | X2!=iProver_Domain_2 ) & ( X1!=iProver_Domain_2 ) & ( X2!=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 & X1=iProver_Domain_1 & X2=iProver_Domain_1 & X3=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 & X1=iProver_Domain_1 & X2=iProver_Domain_2 & X3=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 & X1=iProver_Domain_1 & X3=iProver_Domain_1 ) ) | ( ( X0=iProver_Domain_2 & X1=iProver_Domain_2 & X2=iProver_Domain_2 ) ) | ( ( X0=iProver_Domain_2 & X2=iProver_Domain_2 & X3=iProver_Domain_1 ) ) | ( ( X1=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 | X2!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 | X2!=iProver_Domain_2 ) ) | ( ( X1=iProver_Domain_1 & X2=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X3!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X3!=iProver_Domain_2 ) & ( X0!=iProver_Domain_2 ) ) | ( ( X1=iProver_Domain_1 & X2=iProver_Domain_2 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X3!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X3!=iProver_Domain_2 ) & ( X0!=iProver_Domain_2 ) ) | ( ( X1=iProver_Domain_1 & X2=iProver_Domain_2 & X3=iProver_Domain_2 ) & ( X0!=iProver_Domain_1 ) ) | ( ( X1=iProver_Domain_1 & X3=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 ) & ( X0!=iProver_Domain_2 | X2!=iProver_Domain_1 ) ) | ( ( X1=iProver_Domain_1 & X3=iProver_Domain_2 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X2!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X2!=iProver_Domain_2 ) ) | ( ( X1=iProver_Domain_2 & X2=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X3!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X3!=iProver_Domain_2 ) ) | ( ( X1=iProver_Domain_2 & X2=iProver_Domain_2 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X3!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 ) ) | ( ( X2=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 ) ) | ( ( X2=iProver_Domain_2 & X3=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 ) & ( X0!=iProver_Domain_2 | X1!=iProver_Domain_1 ) ) | ( ( X2=iProver_Domain_2 & X3=iProver_Domain_2 ) & ( X0!=iProver_Domain_1 | X1!=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 | X1!=iProver_Domain_2 ) & ( X0!=iProver_Domain_2 ) ) | ( ( X3=iProver_Domain_1 ) & ( X0!=iProver_Domain_1 ) & ( X0!=iProver_Domain_2 ) ) ) ) ) ). % SZS output end Model
Start of proof for SEU140+2.p %----------------------------------------------------- fof(t63_xboole_1,conjecture,![_G24899, _G24902, _G24905]: (subset(_G24899, _G24902)&disjoint(_G24902, _G24905)=>disjoint(_G24899, _G24905)),file('SEU140+2.p',t63_xboole_1)). fof(d3_tarski,axiom,![_G24976, _G24979]: (subset(_G24976, _G24979)<=>![_G24985]: (in(_G24985, _G24976)=>in(_G24985, _G24979))),file('SEU140+2.p',d3_tarski)). fof(t3_xboole_0,lemma,![_G25040, _G25043]: (~ (~disjoint(_G25040, _G25043)&![_G25051]: ~ (in(_G25051, _G25040)&in(_G25051, _G25043)))& ~ (?[_G25051]: (in(_G25051, _G25040)&in(_G25051, _G25043))&disjoint(_G25040, _G25043))),file('SEU140+2.p',t3_xboole_0)). cnf(1, plain, [-subset(11^[], 12^[])], clausify(t63_xboole_1)). cnf(2, plain, [-disjoint(12^[], 13^[])], clausify(t63_xboole_1)). cnf(3, plain, [disjoint(11^[], 13^[])], clausify(t63_xboole_1)). cnf(4, plain, [subset(_G2576, _G2577), in(_G2581, _G2576), -in(_G2581, _G2577)], clausify(d3_tarski)). cnf(5, plain, [-disjoint(_G2968, _G2969), -in(9^[_G2969, _G2968], _G2968)], clausify(t3_xboole_0)). cnf(6, plain, [-disjoint(_G2968, _G2969), -in(9^[_G2969, _G2968], _G2969)], clausify(t3_xboole_0)). cnf(7, plain, [disjoint(_G2968, _G2969), in(_G2975, _G2968), in(_G2975, _G2969)], clausify(t3_xboole_0)). cnf('1',plain,[disjoint(12^[], 13^[]), in(9^[13^[], 11^[]], 12^[]), in(9^[13^[], 11^[]], 13^[])],start(7,bind([[_G2968, _G2975, _G2969], [12^[], 9^[13^[], 11^[]], 13^[]]]))). cnf('1.1',plain,[-disjoint(12^[], 13^[])],extension(2)). cnf('1.2',plain,[-in(9^[13^[], 11^[]], 12^[]), subset(11^[], 12^[]), in(9^[13^[], 11^[]], 11^[])],extension(4,bind([[_G2577, _G2581, _G2576], [12^[], 9^[13^[], 11^[]], 11^[]]]))). cnf('1.2.1',plain,[-subset(11^[], 12^[])],extension(1)). cnf('1.2.2',plain,[-in(9^[13^[], 11^[]], 11^[]), -disjoint(11^[], 13^[])],extension(5,bind([[_G2968, _G2969], [11^[], 13^[]]]))). cnf('1.2.2.1',plain,[disjoint(11^[], 13^[])],extension(3)). cnf('1.3',plain,[-in(9^[13^[], 11^[]], 13^[]), -disjoint(11^[], 13^[])],extension(6,bind([[_G2968, _G2969], [11^[], 13^[]]]))). cnf('1.3.1',plain,[disjoint(11^[], 13^[])],extension(3)). %----------------------------------------------------- End of proof for SEU140+2.p
Metis uses the following proof steps ...
(* ========================================================================= *) (* A LOGICAL KERNEL FOR FIRST ORDER CLAUSAL THEOREMS *) (* Copyright (c) 2001 Joe Hurd, distributed under the GNU GPL version 2 *) (* ========================================================================= *) signature Thm = sig (* ------------------------------------------------------------------------- *) (* An abstract type of first order logic theorems. *) (* ------------------------------------------------------------------------- *) type thm (* ------------------------------------------------------------------------- *) (* Primitive rules of inference. *) (* ------------------------------------------------------------------------- *) (* ------------------------------------------------------------------------- *) (* *) (* ----- axiom C *) (* C *) (* ------------------------------------------------------------------------- *) val axiom : clause -> thm (* ------------------------------------------------------------------------- *) (* *) (* ----------- assume L *) (* L \/ ~L *) (* ------------------------------------------------------------------------- *) val assume : literal -> thm (* ------------------------------------------------------------------------- *) (* C *) (* -------- subst s *) (* C[s] *) (* ------------------------------------------------------------------------- *) val subst : subst -> thm -> thm (* ------------------------------------------------------------------------- *) (* L \/ C ~L \/ D *) (* --------------------- resolve L *) (* C \/ D *) (* *) (* The literal L must occur in the first theorem, and the literal ~L must *) (* occur in the second theorem. *) (* ------------------------------------------------------------------------- *) val resolve : literal -> thm -> thm -> thm (* ------------------------------------------------------------------------- *) (* *) (* --------- refl t *) (* t = t *) (* ------------------------------------------------------------------------- *) val refl : term -> thm (* ------------------------------------------------------------------------- *) (* *) (* ------------------------ equality L p t *) (* ~(s = t) \/ ~L \/ L' *) (* *) (* where s is the subterm of L at path p, and L' is L with the subterm at *) (* path p being replaced by t. *) (* ------------------------------------------------------------------------- *) val equality : literal -> path -> term -> thm end
SZS status Theorem for data/problems/all/SEU140+2.tptp SZS output start CNFRefutation for data/problems/all/SEU140+2.tptp fof(commutativity_k2_xboole_0, axiom, (! [A, B] : set_union2(A, B) = set_union2(B, A))). fof(d3_xboole_0, axiom, (! [A, B, C] : (C = set_intersection2(A, B) <=> ! [D] : (in(D, C) <=> (in(D, A) & in(D, B)))))). fof(d4_xboole_0, axiom, (! [A, B, C] : (C = set_difference(A, B) <=> ! [D] : (in(D, C) <=> (in(D, A) & ~ in(D, B)))))). fof(d7_xboole_0, axiom, (! [A, B] : (disjoint(A, B) <=> set_intersection2(A, B) = empty_set))). fof(symmetry_r1_xboole_0, axiom, (! [A, B] : (disjoint(A, B) => disjoint(B, A)))). fof(t12_xboole_1, lemma, (! [A, B] : (subset(A, B) => set_union2(A, B) = B))). fof(t1_boole, axiom, (! [A] : set_union2(A, empty_set) = A)). fof(t2_boole, axiom, (! [A] : set_intersection2(A, empty_set) = empty_set)). fof(t36_xboole_1, lemma, (! [A, B] : subset(set_difference(A, B), A))). fof(t39_xboole_1, lemma, (! [A, B] : set_union2(A, set_difference(B, A)) = set_union2(A, B))). fof(t3_boole, axiom, (! [A] : set_difference(A, empty_set) = A)). fof(t3_xboole_0, lemma, (! [A, B] : (~ (~ disjoint(A, B) & ! [C] : ~ (in(C, A) & in(C, B))) & ~ (? [C] : (in(C, A) & in(C, B)) & disjoint(A, B))))). fof(t40_xboole_1, lemma, (! [A, B] : set_difference(set_union2(A, B), B) = set_difference(A, B))). fof(t48_xboole_1, lemma, (! [A, B] : set_difference(A, set_difference(A, B)) = set_intersection2(A, B))). fof(t63_xboole_1, conjecture, (! [A, B, C] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C)))). fof(subgoal_0, plain, (! [A, B, C] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C))), inference(strip, [], [t63_xboole_1])). fof(negate_0_0, plain, (~ ! [A, B, C] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C))), inference(negate, [], [subgoal_0])). fof(normalize_0_0, plain, (! [A, B] : (~ disjoint(A, B) | disjoint(B, A))), inference(canonicalize, [], [symmetry_r1_xboole_0])). fof(normalize_0_1, plain, (! [A, B] : (~ disjoint(A, B) | disjoint(B, A))), inference(specialize, [], [normalize_0_0])). fof(normalize_0_2, plain, (! [A, B] : (~ disjoint(A, B) | ! [C] : (~ in(C, A) | ~ in(C, B))) & ! [A, B] : (disjoint(A, B) | ? [C] : (in(C, A) & in(C, B)))), inference(canonicalize, [], [t3_xboole_0])). fof(normalize_0_3, plain, (! [A, B] : (disjoint(A, B) | ? [C] : (in(C, A) & in(C, B)))), inference(conjunct, [], [normalize_0_2])). fof(normalize_0_4, plain, (! [A, B] : (disjoint(A, B) | ? [C] : (in(C, A) & in(C, B)))), inference(specialize, [], [normalize_0_3])). fof(normalize_0_5, plain, (! [A, B] : ((disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), A)) & (disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), B)))), inference(clausify, [], [normalize_0_4])). fof(normalize_0_6, plain, (! [A, B] : (disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), B))), inference(conjunct, [], [normalize_0_5])). fof(normalize_0_7, plain, (! [A, B, C] : (C != set_intersection2(A, B) <=> ? [D] : (~ in(D, C) <=> (in(D, A) & in(D, B))))), inference(canonicalize, [], [d3_xboole_0])). fof(normalize_0_8, plain, (! [A, B, C] : (C != set_intersection2(A, B) <=> ? [D] : (~ in(D, C) <=> (in(D, A) & in(D, B))))), inference(specialize, [], [normalize_0_7])). fof(normalize_0_9, plain, (! [A, B, C, D] : ((C != set_intersection2(A, B) | ~ in(D, C) | in(D, A)) & (C != set_intersection2(A, B) | ~ in(D, C) | in(D, B)) & (C = set_intersection2(A, B) | in(skolemFOFtoCNF_D_1(A, B, C), A) | in(skolemFOFtoCNF_D_1(A, B, C), C)) & (C = set_intersection2(A, B) | in(skolemFOFtoCNF_D_1(A, B, C), B) | in(skolemFOFtoCNF_D_1(A, B, C), C)) & (C != set_intersection2(A, B) | ~ in(D, A) | ~ in(D, B) | in(D, C)) & (~ in(skolemFOFtoCNF_D_1(A, B, C), A) | ~ in(skolemFOFtoCNF_D_1(A, B, C), B) | ~ in(skolemFOFtoCNF_D_1(A, B, C), C) | C = set_intersection2(A, B)))), inference(clausify, [], [normalize_0_8])). fof(normalize_0_10, plain, (! [A, B, C, D] : (C != set_intersection2(A, B) | ~ in(D, C) | in(D, B))), inference(conjunct, [], [normalize_0_9])). fof(normalize_0_11, plain, (! [A, B] : set_difference(A, set_difference(A, B)) = set_intersection2(A, B)), inference(canonicalize, [], [t48_xboole_1])). fof(normalize_0_12, plain, (! [A, B] : set_difference(A, set_difference(A, B)) = set_intersection2(A, B)), inference(specialize, [], [normalize_0_11])). fof(normalize_0_13, plain, (! [A, B] : set_difference(set_union2(A, B), B) = set_difference(A, B)), inference(canonicalize, [], [t40_xboole_1])). fof(normalize_0_14, plain, (! [A, B] : set_difference(set_union2(A, B), B) = set_difference(A, B)), inference(specialize, [], [normalize_0_13])). fof(normalize_0_15, plain, (! [A, B] : set_union2(A, set_difference(B, A)) = set_union2(A, B)), inference(canonicalize, [], [t39_xboole_1])). fof(normalize_0_16, plain, (! [A, B] : set_union2(A, set_difference(B, A)) = set_union2(A, B)), inference(specialize, [], [normalize_0_15])). fof(normalize_0_17, plain, (! [A, B] : set_union2(A, B) = set_union2(B, A)), inference(canonicalize, [], [commutativity_k2_xboole_0])). fof(normalize_0_18, plain, (! [A, B] : set_union2(A, B) = set_union2(B, A)), inference(specialize, [], [normalize_0_17])). fof(normalize_0_19, plain, (! [A] : set_difference(A, empty_set) = A), inference(canonicalize, [], [t3_boole])). fof(normalize_0_20, plain, (! [A] : set_difference(A, empty_set) = A), inference(specialize, [], [normalize_0_19])). fof(normalize_0_21, plain, (! [A] : set_intersection2(A, empty_set) = empty_set), inference(canonicalize, [], [t2_boole])). fof(normalize_0_22, plain, (! [A] : set_intersection2(A, empty_set) = empty_set), inference(specialize, [], [normalize_0_21])). fof(normalize_0_23, plain, (? [A, B, C] : (~ disjoint(A, C) & disjoint(B, C) & subset(A, B))), inference(canonicalize, [], [negate_0_0])). fof(normalize_0_24, plain, (~ disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4) & disjoint(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) & subset(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), inference(skolemize, [], [normalize_0_23])). fof(normalize_0_25, plain, (subset(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), inference(conjunct, [], [normalize_0_24])). fof(normalize_0_26, plain, (! [A, B] : (~ subset(A, B) | set_union2(A, B) = B)), inference(canonicalize, [], [t12_xboole_1])). fof(normalize_0_27, plain, (! [A, B] : (~ subset(A, B) | set_union2(A, B) = B)), inference(specialize, [], [normalize_0_26])). fof(normalize_0_28, plain, (! [A, B] : (disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), A))), inference(conjunct, [], [normalize_0_5])). fof(normalize_0_29, plain, (! [A, B, C] : (C != set_difference(A, B) <=> ? [D] : (~ in(D, C) <=> (~ in(D, B) & in(D, A))))), inference(canonicalize, [], [d4_xboole_0])). fof(normalize_0_30, plain, (! [A, B, C] : (C != set_difference(A, B) <=> ? [D] : (~ in(D, C) <=> (~ in(D, B) & in(D, A))))), inference(specialize, [], [normalize_0_29])). fof(normalize_0_31, plain, (! [A, B, C, D] : ((C != set_difference(A, B) | ~ in(D, B) | ~ in(D, C)) & (C != set_difference(A, B) | ~ in(D, C) | in(D, A)) & (~ in(skolemFOFtoCNF_D_2(A, B, C), B) | C = set_difference(A, B) | in(skolemFOFtoCNF_D_2(A, B, C), C)) & (C = set_difference(A, B) | in(skolemFOFtoCNF_D_2(A, B, C), A) | in(skolemFOFtoCNF_D_2(A, B, C), C)) & (C != set_difference(A, B) | ~ in(D, A) | in(D, B) | in(D, C)) & (~ in(skolemFOFtoCNF_D_2(A, B, C), A) | ~ in(skolemFOFtoCNF_D_2(A, B, C), C) | C = set_difference(A, B) | in(skolemFOFtoCNF_D_2(A, B, C), B)))), inference(clausify, [], [normalize_0_30])). fof(normalize_0_32, plain, (! [A, B, C, D] : (C != set_difference(A, B) | ~ in(D, B) | ~ in(D, C))), inference(conjunct, [], [normalize_0_31])). fof(normalize_0_33, plain, (! [A, B] : subset(set_difference(A, B), A)), inference(canonicalize, [], [t36_xboole_1])). fof(normalize_0_34, plain, (! [A, B] : subset(set_difference(A, B), A)), inference(specialize, [], [normalize_0_33])). fof(normalize_0_35, plain, (disjoint(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)), inference(conjunct, [], [normalize_0_24])). fof(normalize_0_36, plain, (! [A, B] : (set_intersection2(A, B) != empty_set <=> ~ disjoint(A, B))), inference(canonicalize, [], [d7_xboole_0])). fof(normalize_0_37, plain, (! [A, B] : (set_intersection2(A, B) != empty_set <=> ~ disjoint(A, B))), inference(specialize, [], [normalize_0_36])). fof(normalize_0_38, plain, (! [A, B] : ((set_intersection2(A, B) != empty_set | disjoint(A, B)) & (~ disjoint(A, B) | set_intersection2(A, B) = empty_set))), inference(clausify, [], [normalize_0_37])). fof(normalize_0_39, plain, (! [A, B] : (~ disjoint(A, B) | set_intersection2(A, B) = empty_set)), inference(conjunct, [], [normalize_0_38])). fof(normalize_0_40, plain, (! [A] : set_union2(A, empty_set) = A), inference(canonicalize, [], [t1_boole])). fof(normalize_0_41, plain, (! [A] : set_union2(A, empty_set) = A), inference(specialize, [], [normalize_0_40])). fof(normalize_0_42, plain, (~ disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4)), inference(conjunct, [], [normalize_0_24])). cnf(refute_0_0, plain, (~ disjoint(A, B) | disjoint(B, A)), inference(canonicalize, [], [normalize_0_1])). cnf(refute_0_1, plain, (~ disjoint(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2) | disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4)), inference(subst, [], [refute_0_0 : [bind(A, $fot(skolemFOFtoCNF_C_4)), bind(B, $fot(skolemFOFtoCNF_A_2))]])). cnf(refute_0_2, plain, (disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), B)), inference(canonicalize, [], [normalize_0_6])). cnf(refute_0_3, plain, (disjoint(A, skolemFOFtoCNF_A_2) | in(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2), skolemFOFtoCNF_A_2)), inference(subst, [], [refute_0_2 : [bind(B, $fot(skolemFOFtoCNF_A_2))]])). cnf(refute_0_4, plain, (C != set_intersection2(A, B) | ~ in(D, C) | in(D, B)), inference(canonicalize, [], [normalize_0_10])). cnf(refute_0_5, plain, (set_intersection2(A, B) != set_intersection2(A, B) | ~ in(D, set_intersection2(A, B)) | in(D, B)), inference(subst, [], [refute_0_4 : [bind(C, $fot(set_intersection2(A, B)))]])). cnf(refute_0_6, plain, (set_intersection2(A, B) = set_intersection2(A, B)), introduced(tautology, [refl, [$fot(set_intersection2(A, B))]])). cnf(refute_0_7, plain, (~ in(D, set_intersection2(A, B)) | in(D, B)), inference(resolve, [$cnf($equal(set_intersection2(A, B), set_intersection2(A, B)))], [refute_0_6, refute_0_5])). cnf(refute_0_8, plain, (~ in(X_311, set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) | in(X_311, skolemFOFtoCNF_B_1)), inference(subst, [], [refute_0_7 : [bind(A, $fot(skolemFOFtoCNF_A_2)), bind(B, $fot(skolemFOFtoCNF_B_1)), bind(D, $fot(X_311))]])). cnf(refute_0_9, plain, (set_difference(A, set_difference(A, B)) = set_intersection2(A, B)), inference(canonicalize, [], [normalize_0_12])). cnf(refute_0_10, plain, (set_difference(skolemFOFtoCNF_A_2, set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) = set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), inference(subst, [], [refute_0_9 : [bind(A, $fot(skolemFOFtoCNF_A_2)), bind(B, $fot(skolemFOFtoCNF_B_1))]])). cnf(refute_0_11, plain, (set_difference(set_union2(A, B), B) = set_difference(A, B)), inference(canonicalize, [], [normalize_0_14])). cnf(refute_0_12, plain, (set_difference(set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)), set_union2(X_79, X_80)) = set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))), inference(subst, [], [refute_0_11 : [bind(A, $fot(set_union2(X_80, X_79))), bind(B, $fot(set_union2(X_79, X_80)))]])). cnf(refute_0_13, plain, (set_union2(A, set_difference(B, A)) = set_union2(A, B)), inference(canonicalize, [], [normalize_0_16])). cnf(refute_0_14, plain, (set_union2(A, set_difference(set_union2(X_65, A), A)) = set_union2(A, set_union2(X_65, A))), inference(subst, [], [refute_0_13 : [bind(B, $fot(set_union2(X_65, A)))]])). cnf(refute_0_15, plain, (set_difference(set_union2(X_65, A), A) = set_difference(X_65, A)), inference(subst, [], [refute_0_11 : [bind(A, $fot(X_65)), bind(B, $fot(A))]])). cnf(refute_0_16, plain, (set_difference(set_union2(X_65, A), A) != set_difference(X_65, A) | set_union2(A, set_difference(set_union2(X_65, A), A)) != set_union2(A, set_union2(X_65, A)) | set_union2(A, set_difference(X_65, A)) = set_union2(A, set_union2(X_65, A))), introduced(tautology, [equality, [$cnf($equal(set_union2(A, set_difference(set_union2(X_65, A), A)), set_union2(A, set_union2(X_65, A)))), [0, 1], $fot(set_difference(X_65, A))]])). cnf(refute_0_17, plain, (set_union2(A, set_difference(set_union2(X_65, A), A)) != set_union2(A, set_union2(X_65, A)) | set_union2(A, set_difference(X_65, A)) = set_union2(A, set_union2(X_65, A))), inference(resolve, [$cnf($equal(set_difference(set_union2(X_65, A), A), set_difference(X_65, A)))], [refute_0_15, refute_0_16])). cnf(refute_0_18, plain, (set_union2(A, set_difference(X_65, A)) = set_union2(A, set_union2(X_65, A))), inference(resolve, [$cnf($equal(set_union2(A, set_difference(set_union2(X_65, A), A)), set_union2(A, set_union2(X_65, A))))], [refute_0_14, refute_0_17])). cnf(refute_0_19, plain, (set_union2(A, set_difference(X_65, A)) = set_union2(A, X_65)), inference(subst, [], [refute_0_13 : [bind(B, $fot(X_65))]])). cnf(refute_0_20, plain, (set_union2(A, set_difference(X_65, A)) != set_union2(A, X_65) | set_union2(A, set_difference(X_65, A)) != set_union2(A, set_union2(X_65, A)) | set_union2(A, X_65) = set_union2(A, set_union2(X_65, A))), introduced(tautology, [equality, [$cnf($equal(set_union2(A, set_difference(X_65, A)), set_union2(A, set_union2(X_65, A)))), [0], $fot(set_union2(A, X_65))]])). cnf(refute_0_21, plain, (set_union2(A, set_difference(X_65, A)) != set_union2(A, set_union2(X_65, A)) | set_union2(A, X_65) = set_union2(A, set_union2(X_65, A))), inference(resolve, [$cnf($equal(set_union2(A, set_difference(X_65, A)), set_union2(A, X_65)))], [refute_0_19, refute_0_20])). cnf(refute_0_22, plain, (set_union2(A, X_65) = set_union2(A, set_union2(X_65, A))), inference(resolve, [$cnf($equal(set_union2(A, set_difference(X_65, A)), set_union2(A, set_union2(X_65, A))))], [refute_0_18, refute_0_21])). cnf(refute_0_23, plain, (set_union2(set_union2(X_76, X_65), X_65) = set_union2(set_union2(X_76, X_65), set_union2(X_65, set_union2(X_76, X_65)))), inference(subst, [], [refute_0_22 : [bind(A, $fot(set_union2(X_76, X_65)))]])). cnf(refute_0_24, plain, (set_union2(X_65, X_76) = set_union2(X_65, set_union2(X_76, X_65))), inference(subst, [], [refute_0_22 : [bind(A, $fot(X_65)), bind(X_65, $fot(X_76))]])). cnf(refute_0_25, plain, (X = X), introduced(tautology, [refl, [$fot(X)]])). cnf(refute_0_26, plain, (X != X | X != Y | Y = X), introduced(tautology, [equality, [$cnf($equal(X, X)), [0], $fot(Y)]])). cnf(refute_0_27, plain, (X != Y | Y = X), inference(resolve, [$cnf($equal(X, X))], [refute_0_25, refute_0_26])). cnf(refute_0_28, plain, (set_union2(X_65, X_76) != set_union2(X_65, set_union2(X_76, X_65)) | set_union2(X_65, set_union2(X_76, X_65)) = set_union2(X_65, X_76)), inference(subst, [], [refute_0_27 : [bind(X, $fot(set_union2(X_65, X_76))), bind(Y, $fot(set_union2(X_65, set_union2(X_76, X_65))))]])). cnf(refute_0_29, plain, (set_union2(X_65, set_union2(X_76, X_65)) = set_union2(X_65, X_76)), inference(resolve, [$cnf($equal(set_union2(X_65, X_76), set_union2(X_65, set_union2(X_76, X_65))))], [refute_0_24, refute_0_28])). cnf(refute_0_30, plain, (set_union2(X_65, set_union2(X_76, X_65)) != set_union2(X_65, X_76) | set_union2(set_union2(X_76, X_65), X_65) != set_union2(set_union2(X_76, X_65), set_union2(X_65, set_union2(X_76, X_65))) | set_union2(set_union2(X_76, X_65), X_65) = set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))), introduced(tautology, [equality, [$cnf($equal(set_union2(set_union2(X_76, X_65), X_65), set_union2(set_union2(X_76, X_65), set_union2(X_65, set_union2(X_76, X_65))))), [1, 1], $fot(set_union2(X_65, X_76))]])). cnf(refute_0_31, plain, (set_union2(set_union2(X_76, X_65), X_65) != set_union2(set_union2(X_76, X_65), set_union2(X_65, set_union2(X_76, X_65))) | set_union2(set_union2(X_76, X_65), X_65) = set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))), inference(resolve, [$cnf($equal(set_union2(X_65, set_union2(X_76, X_65)), set_union2(X_65, X_76)))], [refute_0_29, refute_0_30])). cnf(refute_0_32, plain, (set_union2(set_union2(X_76, X_65), X_65) = set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))), inference(resolve, [$cnf($equal(set_union2(set_union2(X_76, X_65), X_65), set_union2(set_union2(X_76, X_65), set_union2(X_65, set_union2(X_76, X_65)))))], [refute_0_23, refute_0_31])). cnf(refute_0_33, plain, (set_union2(A, B) = set_union2(B, A)), inference(canonicalize, [], [normalize_0_18])). cnf(refute_0_34, plain, (set_union2(A, B) != set_union2(B, A) | set_union2(B, A) = set_union2(A, B)), inference(subst, [], [refute_0_27 : [bind(X, $fot(set_union2(A, B))), bind(Y, $fot(set_union2(B, A)))]])). cnf(refute_0_35, plain, (set_union2(B, A) = set_union2(A, B)), inference(resolve, [$cnf($equal(set_union2(A, B), set_union2(B, A)))], [refute_0_33, refute_0_34])). cnf(refute_0_36, plain, (set_union2(set_union2(X_76, X_65), X_65) = set_union2(X_65, set_union2(X_76, X_65))), inference(subst, [], [refute_0_35 : [bind(A, $fot(X_65)), bind(B, $fot(set_union2(X_76, X_65)))]])). cnf(refute_0_37, plain, (Y != X | Y != Z | X = Z), introduced(tautology, [equality, [$cnf($equal(Y, Z)), [0], $fot(X)]])). cnf(refute_0_38, plain, (X != Y | Y != Z | X = Z), inference(resolve, [$cnf($equal(Y, X))], [refute_0_27, refute_0_37])). cnf(refute_0_39, plain, (set_union2(X_65, set_union2(X_76, X_65)) != set_union2(X_65, X_76) | set_union2(set_union2(X_76, X_65), X_65) != set_union2(X_65, set_union2(X_76, X_65)) | set_union2(set_union2(X_76, X_65), X_65) = set_union2(X_65, X_76)), inference(subst, [], [refute_0_38 : [bind(X, $fot(set_union2(set_union2(X_76, X_65), X_65))), bind(Y, $fot(set_union2(X_65, set_union2(X_76, X_65)))), bind(Z, $fot(set_union2(X_65, X_76)))]])). cnf(refute_0_40, plain, (set_union2(X_65, set_union2(X_76, X_65)) != set_union2(X_65, X_76) | set_union2(set_union2(X_76, X_65), X_65) = set_union2(X_65, X_76)), inference(resolve, [$cnf($equal(set_union2(set_union2(X_76, X_65), X_65), set_union2(X_65, set_union2(X_76, X_65))))], [refute_0_36, refute_0_39])). cnf(refute_0_41, plain, (set_union2(set_union2(X_76, X_65), X_65) = set_union2(X_65, X_76)), inference(resolve, [$cnf($equal(set_union2(X_65, set_union2(X_76, X_65)), set_union2(X_65, X_76)))], [refute_0_29, refute_0_40])). cnf(refute_0_42, plain, (set_union2(set_union2(X_76, X_65), X_65) != set_union2(X_65, X_76) | set_union2(set_union2(X_76, X_65), X_65) != set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76)) | set_union2(X_65, X_76) = set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))), introduced(tautology, [equality, [$cnf($equal(set_union2(set_union2(X_76, X_65), X_65), set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76)))), [0], $fot(set_union2(X_65, X_76))]])). cnf(refute_0_43, plain, (set_union2(set_union2(X_76, X_65), X_65) != set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76)) | set_union2(X_65, X_76) = set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))), inference(resolve, [$cnf($equal(set_union2(set_union2(X_76, X_65), X_65), set_union2(X_65, X_76)))], [refute_0_41, refute_0_42])). cnf(refute_0_44, plain, (set_union2(X_65, X_76) = set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))), inference(resolve, [$cnf($equal(set_union2(set_union2(X_76, X_65), X_65), set_union2(set_union2(X_76, X_65), set_union2(X_65, X_76))))], [refute_0_32, refute_0_43])). cnf(refute_0_45, plain, (set_union2(X_79, X_80) = set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80))), inference(subst, [], [refute_0_44 : [bind(X_65, $fot(X_79)), bind(X_76, $fot(X_80))]])). cnf(refute_0_46, plain, (set_union2(X_79, X_80) != set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)) | set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)) = set_union2(X_79, X_80)), inference(subst, [], [refute_0_27 : [bind(X, $fot(set_union2(X_79, X_80))), bind(Y, $fot(set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80))))]])). cnf(refute_0_47, plain, (set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)) = set_union2(X_79, X_80)), inference(resolve, [$cnf($equal(set_union2(X_79, X_80), set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80))))], [refute_0_45, refute_0_46])). cnf(refute_0_48, plain, (set_difference(set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)), set_union2(X_79, X_80)) != set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) | set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)) != set_union2(X_79, X_80) | set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) = set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))), introduced(tautology, [equality, [$cnf($equal(set_difference(set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)), set_union2(X_79, X_80)), set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)))), [0, 0], $fot(set_union2(X_79, X_80))]])). cnf(refute_0_49, plain, (set_difference(set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)), set_union2(X_79, X_80)) != set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) | set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) = set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))), inference(resolve, [$cnf($equal(set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)), set_union2(X_79, X_80)))], [refute_0_47, refute_0_48])). cnf(refute_0_50, plain, (set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) = set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))), inference(resolve, [$cnf($equal(set_difference(set_union2(set_union2(X_80, X_79), set_union2(X_79, X_80)), set_union2(X_79, X_80)), set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))))], [refute_0_12, refute_0_49])). cnf(refute_0_51, plain, (set_difference(X_50, set_difference(X_50, empty_set)) = set_intersection2(X_50, empty_set)), inference(subst, [], [refute_0_9 : [bind(A, $fot(X_50)), bind(B, $fot(empty_set))]])). cnf(refute_0_52, plain, (set_difference(A, empty_set) = A), inference(canonicalize, [], [normalize_0_20])). cnf(refute_0_53, plain, (set_difference(X_50, empty_set) = X_50), inference(subst, [], [refute_0_52 : [bind(A, $fot(X_50))]])). cnf(refute_0_54, plain, (set_difference(X_50, empty_set) != X_50 | set_difference(X_50, set_difference(X_50, empty_set)) != set_intersection2(X_50, empty_set) | set_difference(X_50, X_50) = set_intersection2(X_50, empty_set)), introduced(tautology, [equality, [$cnf($equal(set_difference(X_50, set_difference(X_50, empty_set)), set_intersection2(X_50, empty_set))), [0, 1], $fot(X_50)]])). cnf(refute_0_55, plain, (set_difference(X_50, set_difference(X_50, empty_set)) != set_intersection2(X_50, empty_set) | set_difference(X_50, X_50) = set_intersection2(X_50, empty_set)), inference(resolve, [$cnf($equal(set_difference(X_50, empty_set), X_50))], [refute_0_53, refute_0_54])). cnf(refute_0_56, plain, (set_difference(X_50, X_50) = set_intersection2(X_50, empty_set)), inference(resolve, [$cnf($equal(set_difference(X_50, set_difference(X_50, empty_set)), set_intersection2(X_50, empty_set)))], [refute_0_51, refute_0_55])). cnf(refute_0_57, plain, (set_intersection2(A, empty_set) = empty_set), inference(canonicalize, [], [normalize_0_22])). cnf(refute_0_58, plain, (set_intersection2(X_50, empty_set) = empty_set), inference(subst, [], [refute_0_57 : [bind(A, $fot(X_50))]])). cnf(refute_0_59, plain, (set_difference(X_50, X_50) != set_intersection2(X_50, empty_set) | set_intersection2(X_50, empty_set) != empty_set | set_difference(X_50, X_50) = empty_set), introduced(tautology, [equality, [$cnf(~ $equal(set_difference(X_50, X_50), empty_set)), [0], $fot(set_intersection2(X_50, empty_set))]])). cnf(refute_0_60, plain, (set_difference(X_50, X_50) != set_intersection2(X_50, empty_set) | set_difference(X_50, X_50) = empty_set), inference(resolve, [$cnf($equal(set_intersection2(X_50, empty_set), empty_set))], [refute_0_58, refute_0_59])). cnf(refute_0_61, plain, (set_difference(X_50, X_50) = empty_set), inference(resolve, [$cnf($equal(set_difference(X_50, X_50), set_intersection2(X_50, empty_set)))], [refute_0_56, refute_0_60])). cnf(refute_0_62, plain, (set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) = empty_set), inference(subst, [], [refute_0_61 : [bind(X_50, $fot(set_union2(X_79, X_80)))]])). cnf(refute_0_63, plain, (set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) != empty_set | set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) != set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) | empty_set = set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))), introduced(tautology, [equality, [$cnf($equal(set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)), set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)))), [0], $fot(empty_set)]])). cnf(refute_0_64, plain, (set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) != set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) | empty_set = set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))), inference(resolve, [$cnf($equal(set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)), empty_set))], [refute_0_62, refute_0_63])). cnf(refute_0_65, plain, (set_difference(set_union2(A, set_union2(X_76, A)), set_union2(X_76, A)) = set_difference(A, set_union2(X_76, A))), inference(subst, [], [refute_0_11 : [bind(B, $fot(set_union2(X_76, A)))]])). cnf(refute_0_66, plain, (set_union2(A, X_76) = set_union2(A, set_union2(X_76, A))), inference(subst, [], [refute_0_22 : [bind(X_65, $fot(X_76))]])). cnf(refute_0_67, plain, (set_union2(A, X_76) != set_union2(A, set_union2(X_76, A)) | set_union2(A, set_union2(X_76, A)) = set_union2(A, X_76)), inference(subst, [], [refute_0_27 : [bind(X, $fot(set_union2(A, X_76))), bind(Y, $fot(set_union2(A, set_union2(X_76, A))))]])). cnf(refute_0_68, plain, (set_union2(A, set_union2(X_76, A)) = set_union2(A, X_76)), inference(resolve, [$cnf($equal(set_union2(A, X_76), set_union2(A, set_union2(X_76, A))))], [refute_0_66, refute_0_67])). cnf(refute_0_69, plain, (set_difference(set_union2(A, set_union2(X_76, A)), set_union2(X_76, A)) != set_difference(A, set_union2(X_76, A)) | set_union2(A, set_union2(X_76, A)) != set_union2(A, X_76) | set_difference(set_union2(A, X_76), set_union2(X_76, A)) = set_difference(A, set_union2(X_76, A))), introduced(tautology, [equality, [$cnf($equal(set_difference(set_union2(A, set_union2(X_76, A)), set_union2(X_76, A)), set_difference(A, set_union2(X_76, A)))), [0, 0], $fot(set_union2(A, X_76))]])). cnf(refute_0_70, plain, (set_difference(set_union2(A, set_union2(X_76, A)), set_union2(X_76, A)) != set_difference(A, set_union2(X_76, A)) | set_difference(set_union2(A, X_76), set_union2(X_76, A)) = set_difference(A, set_union2(X_76, A))), inference(resolve, [$cnf($equal(set_union2(A, set_union2(X_76, A)), set_union2(A, X_76)))], [refute_0_68, refute_0_69])). cnf(refute_0_71, plain, (set_difference(set_union2(A, X_76), set_union2(X_76, A)) = set_difference(A, set_union2(X_76, A))), inference(resolve, [$cnf($equal(set_difference(set_union2(A, set_union2(X_76, A)), set_union2(X_76, A)), set_difference(A, set_union2(X_76, A))))], [refute_0_65, refute_0_70])). cnf(refute_0_72, plain, (set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) = set_difference(X_80, set_union2(X_79, X_80))), inference(subst, [], [refute_0_71 : [bind(A, $fot(X_80)), bind(X_76, $fot(X_79))]])). cnf(refute_0_73, plain, (empty_set != set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) | set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) != set_difference(X_80, set_union2(X_79, X_80)) | empty_set = set_difference(X_80, set_union2(X_79, X_80))), introduced(tautology, [equality, [$cnf(~ $equal(empty_set, set_difference(X_80, set_union2(X_79, X_80)))), [0], $fot(set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)))]])). cnf(refute_0_74, plain, (empty_set != set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) | empty_set = set_difference(X_80, set_union2(X_79, X_80))), inference(resolve, [$cnf($equal(set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)), set_difference(X_80, set_union2(X_79, X_80))))], [refute_0_72, refute_0_73])). cnf(refute_0_75, plain, (set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)) != set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80)) | empty_set = set_difference(X_80, set_union2(X_79, X_80))), inference(resolve, [$cnf($equal(empty_set, set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))))], [refute_0_64, refute_0_74])). cnf(refute_0_76, plain, (empty_set = set_difference(X_80, set_union2(X_79, X_80))), inference(resolve, [$cnf($equal(set_difference(set_union2(X_79, X_80), set_union2(X_79, X_80)), set_difference(set_union2(X_80, X_79), set_union2(X_79, X_80))))], [refute_0_50, refute_0_75])). cnf(refute_0_77, plain, (empty_set = set_difference(X_82, set_union2(X_81, X_82))), inference(subst, [], [refute_0_76 : [bind(X_79, $fot(X_81)), bind(X_80, $fot(X_82))]])). cnf(refute_0_78, plain, (set_union2(X_82, X_81) = set_union2(X_81, X_82)), inference(subst, [], [refute_0_33 : [bind(A, $fot(X_82)), bind(B, $fot(X_81))]])). cnf(refute_0_79, plain, (set_union2(X_82, X_81) != set_union2(X_81, X_82) | set_union2(X_81, X_82) = set_union2(X_82, X_81)), inference(subst, [], [refute_0_27 : [bind(X, $fot(set_union2(X_82, X_81))), bind(Y, $fot(set_union2(X_81, X_82)))]])). cnf(refute_0_80, plain, (set_union2(X_81, X_82) = set_union2(X_82, X_81)), inference(resolve, [$cnf($equal(set_union2(X_82, X_81), set_union2(X_81, X_82)))], [refute_0_78, refute_0_79])). cnf(refute_0_81, plain, (empty_set != set_difference(X_82, set_union2(X_81, X_82)) | set_union2(X_81, X_82) != set_union2(X_82, X_81) | empty_set = set_difference(X_82, set_union2(X_82, X_81))), introduced(tautology, [equality, [$cnf($equal(empty_set, set_difference(X_82, set_union2(X_81, X_82)))), [1, 1], $fot(set_union2(X_82, X_81))]])). cnf(refute_0_82, plain, (empty_set != set_difference(X_82, set_union2(X_81, X_82)) | empty_set = set_difference(X_82, set_union2(X_82, X_81))), inference(resolve, [$cnf($equal(set_union2(X_81, X_82), set_union2(X_82, X_81)))], [refute_0_80, refute_0_81])). cnf(refute_0_83, plain, (empty_set = set_difference(X_82, set_union2(X_82, X_81))), inference(resolve, [$cnf($equal(empty_set, set_difference(X_82, set_union2(X_81, X_82))))], [refute_0_77, refute_0_82])). cnf(refute_0_84, plain, (empty_set = set_difference(skolemFOFtoCNF_A_2, set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))), inference(subst, [], [refute_0_83 : [bind(X_81, $fot(skolemFOFtoCNF_B_1)), bind(X_82, $fot(skolemFOFtoCNF_A_2))]])). cnf(refute_0_85, plain, (subset(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), inference(canonicalize, [], [normalize_0_25])). cnf(refute_0_86, plain, (~ subset(A, B) | set_union2(A, B) = B), inference(canonicalize, [], [normalize_0_27])). cnf(refute_0_87, plain, (~ subset(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) | set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) = skolemFOFtoCNF_B_1), inference(subst, [], [refute_0_86 : [bind(A, $fot(skolemFOFtoCNF_A_2)), bind(B, $fot(skolemFOFtoCNF_B_1))]])). cnf(refute_0_88, plain, (set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) = skolemFOFtoCNF_B_1), inference(resolve, [$cnf(subset(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))], [refute_0_85, refute_0_87])). cnf(refute_0_89, plain, (empty_set != set_difference(skolemFOFtoCNF_A_2, set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) | set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) != skolemFOFtoCNF_B_1 | empty_set = set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), introduced(tautology, [equality, [$cnf($equal(empty_set, set_difference(skolemFOFtoCNF_A_2, set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)))), [1, 1], $fot(skolemFOFtoCNF_B_1)]])). cnf(refute_0_90, plain, (empty_set != set_difference(skolemFOFtoCNF_A_2, set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) | empty_set = set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), inference(resolve, [$cnf($equal(set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1), skolemFOFtoCNF_B_1))], [refute_0_88, refute_0_89])). cnf(refute_0_91, plain, (empty_set = set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), inference(resolve, [$cnf($equal(empty_set, set_difference(skolemFOFtoCNF_A_2, set_union2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))))], [refute_0_84, refute_0_90])). cnf(refute_0_92, plain, (empty_set != set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) | set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) = empty_set), inference(subst, [], [refute_0_27 : [bind(X, $fot(empty_set)), bind(Y, $fot(set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)))]])). cnf(refute_0_93, plain, (set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) = empty_set), inference(resolve, [$cnf($equal(empty_set, set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)))], [refute_0_91, refute_0_92])). cnf(refute_0_94, plain, (set_difference(skolemFOFtoCNF_A_2, set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) != set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) | set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) != empty_set | set_difference(skolemFOFtoCNF_A_2, empty_set) = set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), introduced(tautology, [equality, [$cnf($equal(set_difference(skolemFOFtoCNF_A_2, set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))), [0, 1], $fot(empty_set)]])). cnf(refute_0_95, plain, (set_difference(skolemFOFtoCNF_A_2, set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)) != set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) | set_difference(skolemFOFtoCNF_A_2, empty_set) = set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), inference(resolve, [$cnf($equal(set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1), empty_set))], [refute_0_93, refute_0_94])). cnf(refute_0_96, plain, (set_difference(skolemFOFtoCNF_A_2, empty_set) = set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), inference(resolve, [$cnf($equal(set_difference(skolemFOFtoCNF_A_2, set_difference(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)))], [refute_0_10, refute_0_95])). cnf(refute_0_97, plain, (set_difference(skolemFOFtoCNF_A_2, empty_set) = skolemFOFtoCNF_A_2), inference(subst, [], [refute_0_52 : [bind(A, $fot(skolemFOFtoCNF_A_2))]])). cnf(refute_0_98, plain, (set_difference(skolemFOFtoCNF_A_2, empty_set) != set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) | set_difference(skolemFOFtoCNF_A_2, empty_set) != skolemFOFtoCNF_A_2 | skolemFOFtoCNF_A_2 = set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), introduced(tautology, [equality, [$cnf($equal(set_difference(skolemFOFtoCNF_A_2, empty_set), set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))), [0], $fot(skolemFOFtoCNF_A_2)]])). cnf(refute_0_99, plain, (set_difference(skolemFOFtoCNF_A_2, empty_set) != set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) | skolemFOFtoCNF_A_2 = set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), inference(resolve, [$cnf($equal(set_difference(skolemFOFtoCNF_A_2, empty_set), skolemFOFtoCNF_A_2))], [refute_0_97, refute_0_98])). cnf(refute_0_100, plain, (skolemFOFtoCNF_A_2 = set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)), inference(resolve, [$cnf($equal(set_difference(skolemFOFtoCNF_A_2, empty_set), set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)))], [refute_0_96, refute_0_99])). cnf(refute_0_101, plain, (skolemFOFtoCNF_A_2 != set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) | set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) = skolemFOFtoCNF_A_2), inference(subst, [], [refute_0_27 : [bind(X, $fot(skolemFOFtoCNF_A_2)), bind(Y, $fot(set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)))]])). cnf(refute_0_102, plain, (set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) = skolemFOFtoCNF_A_2), inference(resolve, [$cnf($equal(skolemFOFtoCNF_A_2, set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)))], [refute_0_100, refute_0_101])). cnf(refute_0_103, plain, (set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1) != skolemFOFtoCNF_A_2 | ~ in(X_311, skolemFOFtoCNF_A_2) | in(X_311, set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))), introduced(tautology, [equality, [$cnf(~ in(X_311, set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))), [1], $fot(skolemFOFtoCNF_A_2)]])). cnf(refute_0_104, plain, (~ in(X_311, skolemFOFtoCNF_A_2) | in(X_311, set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1))), inference(resolve, [$cnf($equal(set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1), skolemFOFtoCNF_A_2))], [refute_0_102, refute_0_103])). cnf(refute_0_105, plain, (~ in(X_311, skolemFOFtoCNF_A_2) | in(X_311, skolemFOFtoCNF_B_1)), inference(resolve, [$cnf(in(X_311, set_intersection2(skolemFOFtoCNF_A_2, skolemFOFtoCNF_B_1)))], [refute_0_104, refute_0_8])). cnf(refute_0_106, plain, (~ in(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2), skolemFOFtoCNF_A_2) | in(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2), skolemFOFtoCNF_B_1)), inference(subst, [], [refute_0_105 : [bind(X_311, $fot(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2)))]])). cnf(refute_0_107, plain, (disjoint(A, skolemFOFtoCNF_A_2) | in(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2), skolemFOFtoCNF_B_1)), inference(resolve, [$cnf(in(skolemFOFtoCNF_C_2(A, skolemFOFtoCNF_A_2), skolemFOFtoCNF_A_2))], [refute_0_3, refute_0_106])). cnf(refute_0_108, plain, (disjoint(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2) | in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2), skolemFOFtoCNF_B_1)), inference(subst, [], [refute_0_107 : [bind(A, $fot(skolemFOFtoCNF_C_4))]])). cnf(refute_0_109, plain, (disjoint(A, B) | in(skolemFOFtoCNF_C_2(A, B), A)), inference(canonicalize, [], [normalize_0_28])). cnf(refute_0_110, plain, (disjoint(skolemFOFtoCNF_C_4, B) | in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B), skolemFOFtoCNF_C_4)), inference(subst, [], [refute_0_109 : [bind(A, $fot(skolemFOFtoCNF_C_4))]])). cnf(refute_0_111, plain, (C != set_difference(A, B) | ~ in(D, B) | ~ in(D, C)), inference(canonicalize, [], [normalize_0_32])). cnf(refute_0_112, plain, (set_difference(A, B) != set_difference(A, B) | ~ in(D, B) | ~ in(D, set_difference(A, B))), inference(subst, [], [refute_0_111 : [bind(C, $fot(set_difference(A, B)))]])). cnf(refute_0_113, plain, (set_difference(A, B) = set_difference(A, B)), introduced(tautology, [refl, [$fot(set_difference(A, B))]])). cnf(refute_0_114, plain, (~ in(D, B) | ~ in(D, set_difference(A, B))), inference(resolve, [$cnf($equal(set_difference(A, B), set_difference(A, B)))], [refute_0_113, refute_0_112])). cnf(refute_0_115, plain, (~ in(X_332, set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)) | ~ in(X_332, skolemFOFtoCNF_C_4)), inference(subst, [], [refute_0_114 : [bind(A, $fot(skolemFOFtoCNF_B_1)), bind(B, $fot(skolemFOFtoCNF_C_4)), bind(D, $fot(X_332))]])). cnf(refute_0_116, plain, (set_union2(set_difference(X_62, B), set_difference(X_62, set_difference(X_62, B))) = set_union2(set_difference(X_62, B), X_62)), inference(subst, [], [refute_0_13 : [bind(A, $fot(set_difference(X_62, B))), bind(B, $fot(X_62))]])). cnf(refute_0_117, plain, (set_difference(X_62, set_difference(X_62, B)) = set_intersection2(X_62, B)), inference(subst, [], [refute_0_9 : [bind(A, $fot(X_62))]])). cnf(refute_0_118, plain, (set_difference(X_62, set_difference(X_62, B)) != set_intersection2(X_62, B) | set_union2(set_difference(X_62, B), set_difference(X_62, set_difference(X_62, B))) != set_union2(set_difference(X_62, B), X_62) | set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) = set_union2(set_difference(X_62, B), X_62)), introduced(tautology, [equality, [$cnf($equal(set_union2(set_difference(X_62, B), set_difference(X_62, set_difference(X_62, B))), set_union2(set_difference(X_62, B), X_62))), [0, 1], $fot(set_intersection2(X_62, B))]])). cnf(refute_0_119, plain, (set_union2(set_difference(X_62, B), set_difference(X_62, set_difference(X_62, B))) != set_union2(set_difference(X_62, B), X_62) | set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) = set_union2(set_difference(X_62, B), X_62)), inference(resolve, [$cnf($equal(set_difference(X_62, set_difference(X_62, B)), set_intersection2(X_62, B)))], [refute_0_117, refute_0_118])). cnf(refute_0_120, plain, (set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) = set_union2(set_difference(X_62, B), X_62)), inference(resolve, [$cnf($equal(set_union2(set_difference(X_62, B), set_difference(X_62, set_difference(X_62, B))), set_union2(set_difference(X_62, B), X_62)))], [refute_0_116, refute_0_119])). cnf(refute_0_121, plain, (set_union2(set_difference(X_62, B), X_62) = set_union2(X_62, set_difference(X_62, B))), inference(subst, [], [refute_0_35 : [bind(A, $fot(X_62)), bind(B, $fot(set_difference(X_62, B)))]])). cnf(refute_0_122, plain, (set_union2(set_difference(X_62, B), X_62) != set_union2(X_62, set_difference(X_62, B)) | set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) != set_union2(set_difference(X_62, B), X_62) | set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) = set_union2(X_62, set_difference(X_62, B))), introduced(tautology, [equality, [$cnf($equal(set_union2(set_difference(X_62, B), set_intersection2(X_62, B)), set_union2(set_difference(X_62, B), X_62))), [1], $fot(set_union2(X_62, set_difference(X_62, B)))]])). cnf(refute_0_123, plain, (set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) != set_union2(set_difference(X_62, B), X_62) | set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) = set_union2(X_62, set_difference(X_62, B))), inference(resolve, [$cnf($equal(set_union2(set_difference(X_62, B), X_62), set_union2(X_62, set_difference(X_62, B))))], [refute_0_121, refute_0_122])). cnf(refute_0_124, plain, (set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) = set_union2(X_62, set_difference(X_62, B))), inference(resolve, [$cnf($equal(set_union2(set_difference(X_62, B), set_intersection2(X_62, B)), set_union2(set_difference(X_62, B), X_62)))], [refute_0_120, refute_0_123])). cnf(refute_0_125, plain, (subset(set_difference(A, B), A)), inference(canonicalize, [], [normalize_0_34])). cnf(refute_0_126, plain, (subset(set_difference(X_113, B), X_113)), inference(subst, [], [refute_0_125 : [bind(A, $fot(X_113))]])). cnf(refute_0_127, plain, (~ subset(set_difference(X_113, B), X_113) | set_union2(set_difference(X_113, B), X_113) = X_113), inference(subst, [], [refute_0_86 : [bind(A, $fot(set_difference(X_113, B))), bind(B, $fot(X_113))]])). cnf(refute_0_128, plain, (set_union2(set_difference(X_113, B), X_113) = X_113), inference(resolve, [$cnf(subset(set_difference(X_113, B), X_113))], [refute_0_126, refute_0_127])). cnf(refute_0_129, plain, (set_union2(set_difference(X_113, B), X_113) = set_union2(X_113, set_difference(X_113, B))), inference(subst, [], [refute_0_35 : [bind(A, $fot(X_113)), bind(B, $fot(set_difference(X_113, B)))]])). cnf(refute_0_130, plain, (set_union2(set_difference(X_113, B), X_113) != X_113 | set_union2(set_difference(X_113, B), X_113) != set_union2(X_113, set_difference(X_113, B)) | set_union2(X_113, set_difference(X_113, B)) = X_113), introduced(tautology, [equality, [$cnf($equal(set_union2(set_difference(X_113, B), X_113), X_113)), [0], $fot(set_union2(X_113, set_difference(X_113, B)))]])). cnf(refute_0_131, plain, (set_union2(set_difference(X_113, B), X_113) != X_113 | set_union2(X_113, set_difference(X_113, B)) = X_113), inference(resolve, [$cnf($equal(set_union2(set_difference(X_113, B), X_113), set_union2(X_113, set_difference(X_113, B))))], [refute_0_129, refute_0_130])). cnf(refute_0_132, plain, (set_union2(X_113, set_difference(X_113, B)) = X_113), inference(resolve, [$cnf($equal(set_union2(set_difference(X_113, B), X_113), X_113))], [refute_0_128, refute_0_131])). cnf(refute_0_133, plain, (set_union2(X_62, set_difference(X_62, B)) = X_62), inference(subst, [], [refute_0_132 : [bind(X_113, $fot(X_62))]])). cnf(refute_0_134, plain, (set_union2(X_62, set_difference(X_62, B)) != X_62 | set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) != set_union2(X_62, set_difference(X_62, B)) | set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) = X_62), introduced(tautology, [equality, [$cnf($equal(set_union2(set_difference(X_62, B), set_intersection2(X_62, B)), set_union2(X_62, set_difference(X_62, B)))), [1], $fot(X_62)]])). cnf(refute_0_135, plain, (set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) != set_union2(X_62, set_difference(X_62, B)) | set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) = X_62), inference(resolve, [$cnf($equal(set_union2(X_62, set_difference(X_62, B)), X_62))], [refute_0_133, refute_0_134])). cnf(refute_0_136, plain, (set_union2(set_difference(X_62, B), set_intersection2(X_62, B)) = X_62), inference(resolve, [$cnf($equal(set_union2(set_difference(X_62, B), set_intersection2(X_62, B)), set_union2(X_62, set_difference(X_62, B))))], [refute_0_124, refute_0_135])). cnf(refute_0_137, plain, (set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)) = skolemFOFtoCNF_B_1), inference(subst, [], [refute_0_136 : [bind(B, $fot(skolemFOFtoCNF_C_4)), bind(X_62, $fot(skolemFOFtoCNF_B_1))]])). cnf(refute_0_138, plain, (disjoint(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)), inference(canonicalize, [], [normalize_0_35])). cnf(refute_0_139, plain, (~ disjoint(A, B) | set_intersection2(A, B) = empty_set), inference(canonicalize, [], [normalize_0_39])). cnf(refute_0_140, plain, (~ disjoint(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) | set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) = empty_set), inference(subst, [], [refute_0_139 : [bind(A, $fot(skolemFOFtoCNF_B_1)), bind(B, $fot(skolemFOFtoCNF_C_4))]])). cnf(refute_0_141, plain, (set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) = empty_set), inference(resolve, [$cnf(disjoint(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4))], [refute_0_138, refute_0_140])). cnf(refute_0_142, plain, (set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) != empty_set | set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)) != skolemFOFtoCNF_B_1 | set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), empty_set) = skolemFOFtoCNF_B_1), introduced(tautology, [equality, [$cnf($equal(set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)), skolemFOFtoCNF_B_1)), [0, 1], $fot(empty_set)]])). cnf(refute_0_143, plain, (set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)) != skolemFOFtoCNF_B_1 | set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), empty_set) = skolemFOFtoCNF_B_1), inference(resolve, [$cnf($equal(set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), empty_set))], [refute_0_141, refute_0_142])). cnf(refute_0_144, plain, (set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), empty_set) = skolemFOFtoCNF_B_1), inference(resolve, [$cnf($equal(set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), set_intersection2(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)), skolemFOFtoCNF_B_1))], [refute_0_137, refute_0_143])). cnf(refute_0_145, plain, (set_union2(A, empty_set) = A), inference(canonicalize, [], [normalize_0_41])). cnf(refute_0_146, plain, (set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), empty_set) = set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)), inference(subst, [], [refute_0_145 : [bind(A, $fot(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)))]])). cnf(refute_0_147, plain, (set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), empty_set) != set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) | set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), empty_set) != skolemFOFtoCNF_B_1 | set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) = skolemFOFtoCNF_B_1), introduced(tautology, [equality, [$cnf($equal(set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), empty_set), skolemFOFtoCNF_B_1)), [0], $fot(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4))]])). cnf(refute_0_148, plain, (set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), empty_set) != skolemFOFtoCNF_B_1 | set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) = skolemFOFtoCNF_B_1), inference(resolve, [$cnf($equal(set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), empty_set), set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)))], [refute_0_146, refute_0_147])). cnf(refute_0_149, plain, (set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) = skolemFOFtoCNF_B_1), inference(resolve, [$cnf($equal(set_union2(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), empty_set), skolemFOFtoCNF_B_1))], [refute_0_144, refute_0_148])). cnf(refute_0_150, plain, (set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4) != skolemFOFtoCNF_B_1 | ~ in(X_332, skolemFOFtoCNF_B_1) | in(X_332, set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4))), introduced(tautology, [equality, [$cnf(~ in(X_332, set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4))), [1], $fot(skolemFOFtoCNF_B_1)]])). cnf(refute_0_151, plain, (~ in(X_332, skolemFOFtoCNF_B_1) | in(X_332, set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4))), inference(resolve, [$cnf($equal(set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4), skolemFOFtoCNF_B_1))], [refute_0_149, refute_0_150])). cnf(refute_0_152, plain, (~ in(X_332, skolemFOFtoCNF_B_1) | ~ in(X_332, skolemFOFtoCNF_C_4)), inference(resolve, [$cnf(in(X_332, set_difference(skolemFOFtoCNF_B_1, skolemFOFtoCNF_C_4)))], [refute_0_151, refute_0_115])). cnf(refute_0_153, plain, (~ in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B), skolemFOFtoCNF_B_1) | ~ in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B), skolemFOFtoCNF_C_4)), inference(subst, [], [refute_0_152 : [bind(X_332, $fot(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B)))]])). cnf(refute_0_154, plain, (~ in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B), skolemFOFtoCNF_B_1) | disjoint(skolemFOFtoCNF_C_4, B)), inference(resolve, [$cnf(in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, B), skolemFOFtoCNF_C_4))], [refute_0_110, refute_0_153])). cnf(refute_0_155, plain, (~ in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2), skolemFOFtoCNF_B_1) | disjoint(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2)), inference(subst, [], [refute_0_154 : [bind(B, $fot(skolemFOFtoCNF_A_2))]])). cnf(refute_0_156, plain, (disjoint(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2)), inference(resolve, [$cnf(in(skolemFOFtoCNF_C_2(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2), skolemFOFtoCNF_B_1))], [refute_0_108, refute_0_155])). cnf(refute_0_157, plain, (disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4)), inference(resolve, [$cnf(disjoint(skolemFOFtoCNF_C_4, skolemFOFtoCNF_A_2))], [refute_0_156, refute_0_1])). cnf(refute_0_158, plain, (~ disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4)), inference(canonicalize, [], [normalize_0_42])). cnf(refute_0_159, plain, ($false), inference(resolve, [$cnf(disjoint(skolemFOFtoCNF_A_2, skolemFOFtoCNF_C_4))], [refute_0_157, refute_0_158])). SZS output end CNFRefutation for data/problems/all/SEU140+2.tptp
SZS status Theorem for SEU140+2.p SZS output start proof for SEU140+2.p * * * * * * * * * * * * * * * * * * * * * * * * in the following, N is the number of a (sub)theorem E is the current step or the step when a hypothesis or conclusion has been added or modified hyp(N,H,E) means that H is an hypothesis of (sub)theorem N concl(N,C,E) means that C is the conclusion of (sub)theorem N obj_ct(N,C) means that C is a created object or a given constant addhyp(N,H,E) means add H as a new hypothesis for N newconcl(N,C,E) means that the new conclusion of N is C (C replaces the precedent conclusion) a subtheorem N-i or N+i is a subtheorem of the (sub)theorem N N is proved if all N-i have been proved (&-node) or if one N+i have been proved (|-node) the initial theorem is numbered 0 * * * theorem to be proved ![A, B, C]: (subset(A, B)&disjoint(B, C)=>disjoint(A, C)) * * * proof : * * * * * * theoreme 0 * * * * * * *** newconcl(0, ![A, B, C]: (subset(A, B)&disjoint(B, C)=>disjoint(A, C)), 1) *** explanation : initial theorem ------------------------------------------------------- action ini create object(s) z3 z2 z1 *** newconcl(0, subset(z1, z2)&disjoint(z2, z3)=>disjoint(z1, z3), 2) *** because concl((0, ![A, B, C]: (subset(A, B)&disjoint(B, C)=>disjoint(A, C))), 1) *** explanation : the universal variable(s) of the conclusion is(are) instantiated ------------------------------------------------------- rule ! *** addhyp(0, subset(z1, z2), 3) *** addhyp(0, disjoint(z2, z3), 3) *** newconcl(0, disjoint(z1, z3), 3) *** because concl(0, subset(z1, z2)&disjoint(z2, z3)=>disjoint(z1, z3), 2) *** explanation : to prove H=>C, assume H and prove C ------------------------------------------------------- rule => *** addhyp(0, set_intersection2(z2, z3)::empty_set, 4) *** because hyp(0, disjoint(z2, z3), 3) *** explanation : rule if hyp(A, disjoint(B, C), _)then addhyp(A, set_intersection2(B, C)::empty_set, _) built from the definition of disjoint (fof d7_xboole_0 ) ------------------------------------------------------- rule disjoint *** addhyp(0, set_difference(z1, z2)::empty_set, 21) *** because hyp(0, subset(z1, z2), 3), obj_ct(0, z1), obj_ct(0, z2) *** explanation : rule if (hyp(A, subset(B, C), _), obj_ct(A, B), obj_ct(A, C))then addhyp(A, set_difference(B, C)::empty_set, _) built from the axiom l32_xboole_1 ------------------------------------------------------- rule l32_xboole_1_1 *** newconcl(0, set_intersection2(z1, z3)::empty_set, 109) *** because concl(0, disjoint(z1, z3), 3) *** explanation : the conclusion disjoint(z1, z3) is replaced by its definition(fof d7_xboole_0 ) ------------------------------------------------------- rule def_concl_pred *** newconcl(0, seul(set_intersection2(z1, z3)::A, A=empty_set), 110) *** because concl(0, set_intersection2(z1, z3)::empty_set, 109) *** explanation : FX::Y is rewriten only(FX::Z, Z=Y) ------------------------------------------------------- rule concl2pts *** addhyp(0, set_intersection2(z1, z3)::z4, 111), newconcl(0, z4=empty_set, 111) *** because concl(0, seul(set_intersection2(z1, z3)::A, A=empty_set), 110) *** explanation : creation of object z4 and of its definition ------------------------------------------------------- rule concl_only *** addhyp(0, set_intersection2(z3, z1)::z4, 113) *** because hyp(0, set_intersection2(z1, z3)::z4, 111), obj_ct(0, z1), obj_ct(0, z3) *** explanation : rule if (hyp(A, set_intersection2(B, C)::D, _), obj_ct(A, B), obj_ct(A, C))then addhyp(A, set_intersection2(C, B)::D, _) built from the axiom commutativity_k3_xboole_0 ------------------------------------------------------- rule commutativity_k3_xboole_0_1 *** newconcl(0, ![A]: ~in(A, z4), 114) *** because concl(0, z4=empty_set, 111) *** explanation : sufficient condition (rule : d1_xboole_0_1 (fof d1_xboole_0 ) ------------------------------------------------------- rule d1_xboole_0_1_cs create object(s) z5 *** newconcl(0, ~in(z5, z4), 115) *** because concl((0, ![A]: ~in(A, z4)), 114) *** explanation : the universal variable(s) of the conclusion is(are) instantiated ------------------------------------------------------- rule ! *** addhyp(0, in(z5, z4), 116), newconcl(0, false, 116) *** because concl(0, ~in(z5, z4), 115) *** explanation : assume in(z5, z4) and search for a contradiction ------------------------------------------------------- rule concl_not *** addhyp(0, in(z5, z1), 118) *** because hyp(0, set_intersection2(z1, z3)::z4, 111), hyp(0, in(z5, z4), 116), obj_ct(0, z5) *** explanation : rule if (hyp(A, set_intersection2(D, _)::B, _), hyp(A, in(C, B), _), obj_ct(A, C))then addhyp(A, in(C, D), _) built from the definition of set_intersection2 (fof d3_xboole_0 ) ------------------------------------------------------- rule set_intersection2 *** addhyp(0, in(z5, z2), 119) *** because hyp(0, subset(z1, z2), 3), hyp(0, in(z5, z1), 118), obj_ct(0, z5) *** explanation : rule if (hyp(A, subset(B, D), _), hyp(A, in(C, B), _), obj_ct(A, C))then addhyp(A, in(C, D), _) built from the definition of subset (fof d3_tarski ) ------------------------------------------------------- rule subset *** addhyp(0, in(z5, z3), 120) *** because hyp(0, set_intersection2(z3, z1)::z4, 113), hyp(0, in(z5, z4), 116), obj_ct(0, z5) *** explanation : rule if (hyp(A, set_intersection2(D, _)::B, _), hyp(A, in(C, B), _), obj_ct(A, C))then addhyp(A, in(C, D), _) built from the definition of set_intersection2 (fof d3_xboole_0 ) ------------------------------------------------------- rule set_intersection2 *** addhyp(0, in(z5, empty_set), 121) *** because hyp(0, set_intersection2(z2, z3)::empty_set, 4), hyp(0, in(z5, z2), 119), hyp(0, in(z5, z3), 120), obj_ct(0, z5) *** explanation : rule if (hyp(A, set_intersection2(B, D)::E, _), hyp(A, in(C, B), _), hyp(A, in(C, D), _), obj_ct(A, C))then addhyp(A, in(C, E), _) built from the definition of set_intersection2 (fof d3_xboole_0 ) ------------------------------------------------------- rule set_intersection4 *** addhyp(0, false, 122) *** because hyp(0, set_difference(z1, z2)::empty_set, 21), hyp(0, in(z5, empty_set), 121), hyp(0, in(z5, z2), 119), obj_ct(0, z5) *** explanation : rule if (hyp(A, set_difference(_, D)::B, _), hyp(A, in(C, B), _), hyp(A, in(C, D), _), obj_ct(A, C))then addhyp(A, false, _) built from the definition of set_difference (fof d4_xboole_0 ) ------------------------------------------------------- rule set_difference1 *** newconcl(0, true, 123) *** because hyp(0, false, 122), concl(0, false, 116) *** explanation : the conclusion false to be proved is a hypothesis ------------------------------------------------------- rule stop_hyp_concl then the initial theorem is proved * * * * * * * * * * * * * * * * * * * * * * * * SZS output end proof for SEU140+2.p
The domain elements of a model are of the form iN. Function mappings are provided for all tuples of domain elements. Predicate mappings are listed for the true cases.
Constants: abstraction = {(i4, i2)} act = {(i4, i1)} actual_world = {i3, i4} agent = {(i4, i1, i3)} animate = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)} beverage = {(i4, i4)} entity = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3), (i4, i4)} event = {(i4, i1)} eventuality = {(i4, i1)} existent = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3), (i4, i4)} female = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i3, i3), (i4, i3)} food = {(i4, i4)} forename = {(i4, i2)} general = {(i4, i2)} human = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)} human_person = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)} impartial = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3), (i4, i4)} living = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)} mia_forename = {(i4, i2)} nonexistent = {(i4, i1)} nonhuman = {(i4, i2)} nonliving = {(i4, i4)} nonreflexive = {(i4, i1)} object = {(i4, i4)} of = {(i4, i2, i3)} order = {(i4, i1)} organism = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)} past = {(i4, i1)} patient = {(i4, i1, i4)} relation = {(i4, i2)} relname = {(i4, i2)} shake_beverage = {(i4, i4)} singleton = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i1), (i4, i2), (i4, i3), (i4, i4)} specific = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i1), (i4, i3), (i4, i4)} substance_matter = {(i4, i4)} thing = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i1), (i4, i2), (i4, i3), (i4, i4)} unisex = {(i4, i1), (i4, i2), (i4, i4)} woman = {(i1, i3), (i2, i1), (i2, i2), (i2, i4), (i3, i2), (i4, i3)}
a = i1 a_holds = {i2} a_key = {i2} a_nonce = {i1} a_stored = {i1} an_a_nonce = i1 an_intruder_nonce = i1 at = i2 b = i2 b_holds = {i2} b_stored = {i1, i2} bt = i1 encrypt = (%x. _) ((i1, i1) := i1, (i1, i2) := i1, (i2, i1) := i1, (i2, i2) := i1) fresh_intruder_nonce = {i1} fresh_to_b = {i1} generate_b_nonce = (%x. _)(i1 := i1, i2 := i1) generate_expiration_time = (%x. _)(i1 := i1, i2 := i1) generate_intruder_nonce = (%x. _)(i1 := i1, i2 := i1) generate_key = (%x. _)(i1 := i2, i2 := i2) intruder_holds = {i2} intruder_message = {i1, i2} key = (%x. _) ((i1, i1) := i2, (i1, i2) := i2, (i2, i1) := i2, (i2, i2) := i2) message = {i1} pair = (%x. _) ((i1, i1) := i2, (i1, i2) := i1, (i2, i1) := i1, (i2, i2) := i2) party_of_protocol = {i1, i2} quadruple = (%x. _) ((i1, i1, i1, i1) := i1, (i1, i1, i1, i2) := i1, (i1, i1, i2, i1) := i1, (i1, i1, i2, i2) := i1, (i1, i2, i1, i1) := i1, (i1, i2, i1, i2) := i1, (i1, i2, i2, i1) := i1, (i1, i2, i2, i2) := i1, (i2, i1, i1, i1) := i1, (i2, i1, i1, i2) := i1, (i2, i1, i2, i1) := i1, (i2, i1, i2, i2) := i1, (i2, i2, i1, i1) := i1, (i2, i2, i1, i2) := i1, (i2, i2, i2, i1) := i1, (i2, i2, i2, i2) := i1) sent = (%x. _) ((i1, i1, i1) := i1, (i1, i1, i2) := i1, (i1, i2, i1) := i1, (i1, i2, i2) := i1, (i2, i1, i1) := i1, (i2, i1, i2) := i1, (i2, i2, i1) := i1, (i2, i2, i2) := i1) t = i2 t_holds = {i2} triple = (%x. _) ((i1, i1, i1) := i2, (i1, i1, i2) := i1, (i1, i2, i1) := i1, (i1, i2, i2) := i1, (i2, i1, i1) := i2, (i2, i1, i2) := i1, (i2, i2, i1) := i1, (i2, i2, i2) := i1)
% domain size is 1 disbanding_rate(!1,!1) = !1 efficient_producers = !1 environment(!1) <=> $true first_movers = !1 founding_rate(!1,!1) = !1 greater(!1,!1) <=> $false greater_or_equal(!1,!1) <=> $true growth_rate(!1,!1) = !1 in_environment(!1,!1) <=> $true stable(!1) <=> $true subpopulations(!1,!1,!1,!1) <=> $true
% domain size is 1 a_holds(X1) a_stored(X1) b_holds(X1) b_stored(X1) fresh_to_b(X1) message(X1) party_of_protocol(X1) t_holds(X1)
% SZS status Theorem for SYN075+1 % SZS output start Proof for SYN075+1 fof(f509,plain,( $false), inference(subsumption_resolution,[],[f508,f145])). fof(f145,plain,( big_f($sk3,$sk4)), inference(backtracking_split_refutation,[],[f69,f70_D,f124])). fof(f124,plain,( $false | $spl1), inference(subsumption_resolution,[],[f123,f110])). fof(f110,plain,( ( ! [X0] : (~big_f($sk3,X0)) ) | $spl1), inference(forward_demodulation,[],[f106,f92])). fof(f92,plain,( ( ! [X0] : ($sk2($sk3,X0) = $sk3) ) | $spl1), inference(factoring,[],[f85])). fof(f85,plain,( ( ! [X2,X3] : ($sk2(X2,X3) = X2 | $sk2(X2,X3) = $sk3) ) | $spl1), inference(resolution,[],[f82,f15])). fof(f15,plain,( ( ! [X2,X3] : (~big_f(X2,X3) | $sk3 = X2) )), inference(cnf_transformation,[],[f10])). fof(f10,plain,( ! [X2,X3] : ((~big_f(X2,X3) | ($sk3 = X2 & $sk4 = X3)) & ($sk3 != X2 | $sk4 != X3 | big_f(X2,X3)))), inference(skolemisation,[status(esa)],[f9])). fof(f9,plain,( ? [X0,X1] : ! [X2,X3] : ((~big_f(X2,X3) | (X0 = X2 & X1 = X3)) & (X0 != X2 | X1 != X3 | big_f(X2,X3)))), inference(flattening,[],[f8])). fof(f8,plain,( ? [X0,X1] : ! [X2,X3] : ((~big_f(X2,X3) | (X0 = X2 & X1 = X3)) & ((X0 != X2 | X1 != X3) | big_f(X2,X3)))), inference(nnf_transformation,[],[f1])). fof(f1,axiom,( ? [X0,X1] : ! [X2,X3] : (big_f(X2,X3) <=> (X0 = X2 & X1 = X3))), file('/tmp/SystemOnTPTP10164/SYN075+1.tptp',pel52_1)). fof(f82,plain,( ( ! [X4,X0] : (big_f($sk2(X4,X0),X0) | $sk2(X4,X0) = X4) ) | $spl1), inference(subsumption_resolution,[],[f73,f70])). fof(f73,plain,( ( ! [X4,X0] : (big_f($sk2(X4,X0),X0) | $sk0(X0) != X0 | $sk2(X4,X0) = X4) ) | $spl1), inference(backward_demodulation,[],[f70,f13])). fof(f13,plain,( ( ! [X4,X0] : ($sk0(X0) != X0 | $sk2(X4,X0) = X4 | big_f($sk2(X4,X0),$sk0(X0))) )), inference(cnf_transformation,[],[f7])). fof(f7,plain,( ! [X0] : ((! [X3] : ((~big_f(X3,$sk0(X0)) | $sk1(X0) = X3) & ($sk1(X0) != X3 | big_f(X3,$sk0(X0)))) | $sk0(X0) = X0) & (! [X4] : ((big_f($sk2(X4,X0),$sk0(X0)) | $sk2(X4,X0) = X4) & (~big_f($sk2(X4,X0),$sk0(X0)) | $sk2(X4,X0) != X4)) | $sk0(X0) != X0))), inference(skolemisation,[status(esa)],[f6])). fof(f6,plain,( ! [X0] : ? [X1] : ((? [X2] : ! [X3] : ((~big_f(X3,X1) | X2 = X3) & (X2 != X3 | big_f(X3,X1))) | X0 = X1) & (! [X4] : ? [X5] : ((big_f(X5,X1) | X4 = X5) & (~big_f(X5,X1) | X4 != X5)) | X0 != X1))), inference(rectify,[],[f5])). fof(f5,plain,( ! [X0] : ? [X1] : ((? [X2] : ! [X3] : ((~big_f(X3,X1) | X2 = X3) & (X2 != X3 | big_f(X3,X1))) | X0 = X1) & (! [X2] : ? [X3] : ((big_f(X3,X1) | X2 = X3) & (~big_f(X3,X1) | X2 != X3)) | X0 != X1))), inference(nnf_transformation,[],[f4])). fof(f4,plain,( ! [X0] : ? [X1] : (? [X2] : ! [X3] : (big_f(X3,X1) <=> X2 = X3) <~> X0 = X1)), inference(ennf_transformation,[],[f3])). fof(f3,plain,( ~? [X0] : ! [X1] : (? [X2] : ! [X3] : (big_f(X3,X1) <=> X2 = X3) <=> X0 = X1)), inference(rectify,[],[f2])). fof(f2,negated_conjecture,( ~? [X1] : ! [X3] : (? [X0] : ! [X2] : (big_f(X2,X3) <=> X0 = X2) <=> X1 = X3)), file('/tmp/SystemOnTPTP10164/SYN075+1.tptp',pel52)). fof(f106,plain,( ( ! [X0] : (~big_f($sk2($sk3,X0),X0)) ) | $spl1), inference(resolution,[],[f92,f83])). fof(f83,plain,( ( ! [X4,X0] : ($sk2(X4,X0) != X4 | ~big_f($sk2(X4,X0),X0)) ) | $spl1), inference(subsumption_resolution,[],[f74,f70])). fof(f74,plain,( ( ! [X4,X0] : (~big_f($sk2(X4,X0),X0) | $sk0(X0) != X0 | $sk2(X4,X0) != X4) ) | $spl1), inference(backward_demodulation,[],[f70,f14])). fof(f14,plain,( ( ! [X4,X0] : ($sk2(X4,X0) != X4 | $sk0(X0) != X0 | ~big_f($sk2(X4,X0),$sk0(X0))) )), inference(cnf_transformation,[],[f7])). fof(f123,plain,( big_f($sk3,$sk4) | $spl1), inference(forward_demodulation,[],[f118,f92])). fof(f118,plain,( ( ! [X2] : (big_f($sk2($sk3,X2),$sk4)) ) | $spl1), inference(resolution,[],[f116,f92])). fof(f116,plain,( ( ! [X0] : ($sk3 != X0 | big_f(X0,$sk4)) ) | $spl1), inference(forward_demodulation,[],[f112,f70])). fof(f112,plain,( ( ! [X0] : (big_f(X0,$sk0($sk4)) | $sk3 != X0) ) | $spl1), inference(resolution,[],[f17,f70])). fof(f17,plain,( ( ! [X2,X3] : ($sk4 != X3 | big_f(X2,X3) | $sk3 != X2) )), inference(cnf_transformation,[],[f10])). fof(f70,plain,( ( ! [X0] : ($sk0(X0) = X0) ) | $spl1), inference(cnf_transformation,[],[f70_D])). fof(f70_D,plain,( ( ! [X0] : ($sk0(X0) = X0) ) <=> ~$spl1), introduced(backtracking_splitting_component,[])). fof(f69,plain,( ( ! [X0] : (big_f($sk3,$sk4) | $sk0(X0) = X0) )), inference(duplicate_literal_removal,[],[f68])). fof(f68,plain,( ( ! [X0] : (big_f($sk3,$sk4) | $sk0(X0) = X0 | $sk0(X0) = X0) )), inference(superposition,[],[f34,f21])). fof(f21,plain,( ( ! [X2] : ($sk1(X2) = $sk3 | $sk0(X2) = X2) )), inference(resolution,[],[f18,f15])). fof(f18,plain,( ( ! [X0] : (big_f($sk1(X0),$sk0(X0)) | $sk0(X0) = X0) )), inference(equality_resolution,[],[f12])). fof(f12,plain,( ( ! [X0,X3] : ($sk1(X0) != X3 | big_f(X3,$sk0(X0)) | $sk0(X0) = X0) )), inference(cnf_transformation,[],[f7])). fof(f34,plain,( ( ! [X0] : (big_f($sk1(X0),$sk4) | $sk0(X0) = X0) )), inference(duplicate_literal_removal,[],[f29])). fof(f29,plain,( ( ! [X0] : (big_f($sk1(X0),$sk4) | $sk0(X0) = X0 | $sk0(X0) = X0) )), inference(superposition,[],[f18,f20])). fof(f20,plain,( ( ! [X1] : ($sk0(X1) = X1 | $sk0(X1) = $sk4) )), inference(resolution,[],[f18,f16])). fof(f16,plain,( ( ! [X2,X3] : (~big_f(X2,X3) | $sk4 = X3) )), inference(cnf_transformation,[],[f10])). fof(f508,plain,( ~big_f($sk3,$sk4)), inference(forward_demodulation,[],[f507,f24])). fof(f24,plain,( $sk0($sk4) = $sk4), inference(factoring,[],[f20])). fof(f507,plain,( ~big_f($sk3,$sk0($sk4))), inference(forward_demodulation,[],[f506,f293])). fof(f293,plain,( $sk2($sk3,$sk4) = $sk3), inference(factoring,[],[f234])). fof(f234,plain,( ( ! [X1] : ($sk2(X1,$sk4) = X1 | $sk2(X1,$sk4) = $sk3) )), inference(resolution,[],[f64,f15])). fof(f64,plain,( ( ! [X3] : (big_f($sk2(X3,$sk4),$sk4) | $sk2(X3,$sk4) = X3) )), inference(forward_demodulation,[],[f57,f24])). fof(f57,plain,( ( ! [X3] : ($sk2(X3,$sk4) = X3 | big_f($sk2(X3,$sk4),$sk0($sk4))) )), inference(resolution,[],[f13,f24])). fof(f506,plain,( ~big_f($sk2($sk3,$sk4),$sk0($sk4))), inference(subsumption_resolution,[],[f496,f16])). fof(f496,plain,( $sk0($sk4) != $sk4 | ~big_f($sk2($sk3,$sk4),$sk0($sk4))), inference(resolution,[],[f14,f293])). % SZS output end Proof for SYN075+1
% SZS status Theorem for SEU140+2 % SZS output start Proof for SEU140+2 fof(f7254,plain,( $false), inference(subsumption_resolution,[],[f7250,f129])). fof(f129,plain,( subset(sK0,sK1)), inference(cnf_transformation,[],[f99])). fof(f99,plain,( subset(sK0,sK1) & disjoint(sK1,sK2) & ~disjoint(sK0,sK2)), inference(skolemisation,[status(esa)],[f71])). fof(f71,plain,( ? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))), inference(flattening,[],[f70])). fof(f70,plain,( ? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))), inference(ennf_transformation,[],[f51])). fof(f51,negated_conjecture,( ~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))), file('Problems/SEU/SEU140+2.p',t63_xboole_1)). fof(f7250,plain,( ~subset(sK0,sK1)), inference(resolution,[],[f7008,f131])). fof(f131,plain,( ~disjoint(sK0,sK2)), inference(cnf_transformation,[],[f99])). fof(f7008,plain,( ( ! [X0] : (disjoint(X0,sK2) | ~subset(X0,sK1)) )), inference(superposition,[],[f6994,f145])). fof(f145,plain,( ( ! [X0,X1] : (set_intersection2(X0,X1) = X0 | ~subset(X0,X1)) )), inference(cnf_transformation,[],[f75])). fof(f75,plain,( ! [X0,X1] : (~subset(X0,X1) | set_intersection2(X0,X1) = X0)), inference(ennf_transformation,[],[f34])). fof(f34,axiom,( ! [X0,X1] : (subset(X0,X1) => set_intersection2(X0,X1) = X0)), file('Problems/SEU/SEU140+2.p',t28_xboole_1)). fof(f6994,plain,( ( ! [X0] : (disjoint(set_intersection2(X0,sK1),sK2)) )), inference(duplicate_literal_removal,[],[f6963])). fof(f6963,plain,( ( ! [X0] : (disjoint(set_intersection2(X0,sK1),sK2) | disjoint(set_intersection2(X0,sK1),sK2)) )), inference(resolution,[],[f988,f530])). fof(f530,plain,( ( ! [X1] : (~in(sK4(sK2,X1),sK1) | disjoint(X1,sK2)) )), inference(resolution,[],[f522,f143])). fof(f143,plain,( ( ! [X0,X1] : (in(sK4(X1,X0),X1) | disjoint(X0,X1)) )), inference(cnf_transformation,[],[f101])). fof(f101,plain,( ! [X0,X1] : ((disjoint(X0,X1) | (in(sK4(X1,X0),X0) & in(sK4(X1,X0),X1))) & (! [X3] : (~in(X3,X0) | ~in(X3,X1)) | ~disjoint(X0,X1)))), inference(skolemisation,[status(esa)],[f74])). fof(f74,plain,( ! [X0,X1] : ((disjoint(X0,X1) | ? [X2] : (in(X2,X0) & in(X2,X1))) & (! [X3] : (~in(X3,X0) | ~in(X3,X1)) | ~disjoint(X0,X1)))), inference(ennf_transformation,[],[f60])). fof(f60,plain,( ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X3] : (in(X3,X0) & in(X3,X1)) & disjoint(X0,X1)))), inference(flattening,[],[f58])). fof(f58,plain,( ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X3] : (in(X3,X0) & in(X3,X1)) & disjoint(X0,X1)))), inference(rectify,[],[f43])). fof(f43,axiom,( ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))), file('Problems/SEU/SEU140+2.p',t3_xboole_0)). fof(f522,plain,( ( ! [X20] : (~in(X20,sK2) | ~in(X20,sK1)) )), inference(resolution,[],[f144,f130])). fof(f130,plain,( disjoint(sK1,sK2)), inference(cnf_transformation,[],[f99])). fof(f144,plain,( ( ! [X0,X3,X1] : (~disjoint(X0,X1) | ~in(X3,X1) | ~in(X3,X0)) )), inference(cnf_transformation,[],[f101])). fof(f988,plain,( ( ! [X4,X2,X3] : (in(sK4(X2,set_intersection2(X3,X4)),X4) | disjoint(set_intersection2(X3,X4),X2)) )), inference(resolution,[],[f214,f142])). fof(f142,plain,( ( ! [X0,X1] : (in(sK4(X1,X0),X0) | disjoint(X0,X1)) )), inference(cnf_transformation,[],[f101])). fof(f214,plain,( ( ! [X0,X3,X1] : (~in(X3,set_intersection2(X0,X1)) | in(X3,X1)) )), inference(equality_resolution,[],[f191])). fof(f191,plain,( ( ! [X2,X0,X3,X1] : (in(X3,X1) | ~in(X3,X2) | set_intersection2(X0,X1) != X2) )), inference(cnf_transformation,[],[f118])). fof(f118,plain,( ! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X0) | ~in(X3,X1) | in(X3,X2)))) & (((in(sK8(X2,X1,X0),X2) | (in(sK8(X2,X1,X0),X0) & in(sK8(X2,X1,X0),X1))) & (~in(sK8(X2,X1,X0),X2) | ~in(sK8(X2,X1,X0),X0) | ~in(sK8(X2,X1,X0),X1))) | set_intersection2(X0,X1) = X2))), inference(skolemisation,[status(esa)],[f117])). fof(f117,plain,( ! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X0) | ~in(X3,X1) | in(X3,X2)))) & (? [X4] : ((in(X4,X2) | (in(X4,X0) & in(X4,X1))) & (~in(X4,X2) | ~in(X4,X0) | ~in(X4,X1))) | set_intersection2(X0,X1) = X2))), inference(rectify,[],[f116])). fof(f116,plain,( ! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X0) | ~in(X3,X1) | in(X3,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | ~in(X3,X0) | ~in(X3,X1))) | set_intersection2(X0,X1) = X2))), inference(flattening,[],[f115])). fof(f115,plain,( ! [X0,X1,X2] : ((set_intersection2(X0,X1) != X2 | ! [X3] : ((~in(X3,X2) | (in(X3,X0) & in(X3,X1))) & ((~in(X3,X0) | ~in(X3,X1)) | in(X3,X2)))) & (? [X3] : ((in(X3,X2) | (in(X3,X0) & in(X3,X1))) & (~in(X3,X2) | (~in(X3,X0) | ~in(X3,X1)))) | set_intersection2(X0,X1) = X2))), inference(nnf_transformation,[],[f9])). fof(f9,axiom,( ! [X0,X1,X2] : (set_intersection2(X0,X1) = X2 <=> ! [X3] : (in(X3,X2) <=> (in(X3,X0) & in(X3,X1))))), file('Problems/SEU/SEU140+2.p',d3_xboole_0)). % SZS output end Proof for SEU140+2
% SZS status Theorem for SEU140+2 % SZS output start Proof for SEU140+2 fof(f1999,plain,( $false), inference(unit_resulting_resolution,[],[f130,f1740,f1883,f144])). fof(f144,plain,( ( ! [X0,X3,X1] : (~disjoint(X0,X1) | ~in(X3,X1) | ~in(X3,X0)) )), inference(cnf_transformation,[],[f101])). fof(f101,plain,( ! [X0,X1] : ((disjoint(X0,X1) | (in(sK4(X1,X0),X0) & in(sK4(X1,X0),X1))) & (! [X3] : (~in(X3,X0) | ~in(X3,X1)) | ~disjoint(X0,X1)))), inference(skolemisation,[status(esa)],[f74])). fof(f74,plain,( ! [X0,X1] : ((disjoint(X0,X1) | ? [X2] : (in(X2,X0) & in(X2,X1))) & (! [X3] : (~in(X3,X0) | ~in(X3,X1)) | ~disjoint(X0,X1)))), inference(ennf_transformation,[],[f60])). fof(f60,plain,( ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X3] : (in(X3,X0) & in(X3,X1)) & disjoint(X0,X1)))), inference(flattening,[],[f58])). fof(f58,plain,( ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X3] : (in(X3,X0) & in(X3,X1)) & disjoint(X0,X1)))), inference(rectify,[],[f43])). fof(f43,axiom,( ! [X0,X1] : (~(~disjoint(X0,X1) & ! [X2] : ~(in(X2,X0) & in(X2,X1))) & ~(? [X2] : (in(X2,X0) & in(X2,X1)) & disjoint(X0,X1)))), file('Problems/SEU/SEU140+2.p',t3_xboole_0)). fof(f1883,plain,( in(sK4(sK2,sK0),sK1)), inference(unit_resulting_resolution,[],[f129,f1742,f1615])). fof(f1615,plain,( ( ! [X2,X0,X1] : (~subset(X1,X2) | ~in(X0,X1) | in(X0,X2)) )), inference(literal_reordering,[],[f1614])). fof(f1614,plain,( ( ! [X2,X0,X1] : (in(X0,X2) | ~in(X0,X1) | ~subset(X1,X2)) )), inference(instance_generation,[],[f184])). fof(f184,plain,( ( ! [X2,X0,X1] : (in(X2,X1) | ~in(X2,X0) | ~subset(X0,X1)) )), inference(cnf_transformation,[],[f114])). fof(f114,plain,( ! [X0,X1] : ((~subset(X0,X1) | ! [X2] : (~in(X2,X0) | in(X2,X1))) & ((in(sK7(X1,X0),X0) & ~in(sK7(X1,X0),X1)) | subset(X0,X1)))), inference(skolemisation,[status(esa)],[f113])). fof(f113,plain,( ! [X0,X1] : ((~subset(X0,X1) | ! [X2] : (~in(X2,X0) | in(X2,X1))) & (? [X3] : (in(X3,X0) & ~in(X3,X1)) | subset(X0,X1)))), inference(rectify,[],[f112])). fof(f112,plain,( ! [X0,X1] : ((~subset(X0,X1) | ! [X2] : (~in(X2,X0) | in(X2,X1))) & (? [X2] : (in(X2,X0) & ~in(X2,X1)) | subset(X0,X1)))), inference(nnf_transformation,[],[f96])). fof(f96,plain,( ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (~in(X2,X0) | in(X2,X1)))), inference(ennf_transformation,[],[f8])). fof(f8,axiom,( ! [X0,X1] : (subset(X0,X1) <=> ! [X2] : (in(X2,X0) => in(X2,X1)))), file('Problems/SEU/SEU140+2.p',d3_tarski)). fof(f1742,plain,( in(sK4(sK2,sK0),sK0)), inference(unit_resulting_resolution,[],[f131,f1654])). fof(f1654,plain,( ( ! [X37,X38] : (disjoint(X37,X38) | in(sK4(X38,X37),X37)) )), inference(literal_reordering,[],[f1653])). fof(f1653,plain,( ( ! [X37,X38] : (in(sK4(X38,X37),X37) | disjoint(X37,X38)) )), inference(instance_generation,[],[f142])). fof(f142,plain,( ( ! [X0,X1] : (in(sK4(X1,X0),X0) | disjoint(X0,X1)) )), inference(cnf_transformation,[],[f101])). fof(f131,plain,( ~disjoint(sK0,sK2)), inference(cnf_transformation,[],[f99])). fof(f99,plain,( subset(sK0,sK1) & disjoint(sK1,sK2) & ~disjoint(sK0,sK2)), inference(skolemisation,[status(esa)],[f71])). fof(f71,plain,( ? [X0,X1,X2] : (subset(X0,X1) & disjoint(X1,X2) & ~disjoint(X0,X2))), inference(flattening,[],[f70])). fof(f70,plain,( ? [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) & ~disjoint(X0,X2))), inference(ennf_transformation,[],[f51])). fof(f51,negated_conjecture,( ~! [X0,X1,X2] : ((subset(X0,X1) & disjoint(X1,X2)) => disjoint(X0,X2))), file('Problems/SEU/SEU140+2.p',t63_xboole_1)). fof(f129,plain,( subset(sK0,sK1)), inference(cnf_transformation,[],[f99])). fof(f1740,plain,( in(sK4(sK2,sK0),sK2)), inference(unit_resulting_resolution,[],[f131,f1651])). fof(f1651,plain,( ( ! [X35,X36] : (disjoint(X35,X36) | in(sK4(X36,X35),X36)) )), inference(literal_reordering,[],[f1650])). fof(f1650,plain,( ( ! [X35,X36] : (in(sK4(X36,X35),X36) | disjoint(X35,X36)) )), inference(instance_generation,[],[f143])). fof(f143,plain,( ( ! [X0,X1] : (in(sK4(X1,X0),X1) | disjoint(X0,X1)) )), inference(cnf_transformation,[],[f101])). fof(f130,plain,( disjoint(sK1,sK2)), inference(cnf_transformation,[],[f99])). % SZS output end Proof for SEU140+2
% SZS answers Tuple [[s__agent__m,s__experiencer__m]|_] for CSR082+1